Less Wrong is a community blog devoted to refining the art of human rationality. Please visit our About page for more information.
Last year, AlexMennen ran an iterated prisoner's dilemma tournament with bots that could see each other's source code, which was dubbed a "program equilibrium" tournament. This year, I will be running a similar tournament. Here's how it's going to work: Anyone can submit a bot that plays the iterated PD against other bots. Bots can not only remember previous rounds, as in the standard iterated PD, but also run perfect simulations of their opponent before making a move. Please see the github repo for the full list of rules and a brief tutorial.
There are a few key differences this year:
1) The tournament is in Haskell rather than Scheme.
2) The time limit for each round is shorter (5 seconds rather than 10) but the penalty for not outputting Cooperate or Defect within the time limit has been reduced.
3) Bots cannot directly see each other's source code, but they can run their opponent, specifying the initial conditions of the simulation, and then observe the output.
All submissions should be emailed to firstname.lastname@example.org or PM'd to me here on LessWrong by September 1st, 2014. LW users with 50+ karma who want to participate but do not know Haskell can PM me with an algorithm/psuedocode, and I will translate it into a bot for them. (If there is a flood of such requests, I would appreciate some volunteers to help me out.)
The data-generating mechanism and the joint distribution of variables
It is possible to create arbitrarily complicated mathematical structures to describe empirical research. If the logic is done correctly, these structures are all completely valid, but they are only useful if the mathematical objects correctly represent the things in the real world that we want to learn about. Whenever someone tells you about a new framework which has been found to be mathematically valid, the first question you should ask yourself is whether the new framework allows you to correctly represent the important aspects of phenomena you are studying.
When we are interested in causal questions, the phenomenon we are studying is called "the data generating mechanism". The data generating mechanism is the causal force of nature that assigns value to variables. Questions about the data generating mechanism include “Which variable has its value assigned first?”, “What variables from the past are taken into consideration when nature assigns the value of a variable?” and “What is the causal effect of treatment”.
We can never observe the data generating mechanism. Instead, we observe something different, which we call “The joint distribution of observed variables”. The joint distribution is created when the data generating mechanism assigns value to variables in individuals. All questions about how whether observed variables are correlated or independent, and how about strongly they are correlated, are questions about the joint distribution.
The basic problem of causal inference is that the relationship between the set of possible data generating mechanisms, and the joint distribution of variables, is many-to-one.
Imagine you have data on all observable variables for all individuals in the world. You can just look at your data and know everything there is to know about the joint distribution. You don’t need estimators, and you don’t need to worry about limited samples. Anything you need to know about the joint distribution can just be looked up. Now ask yourself: Can you learn anything about causal effects from this data?
Consider the two graphs below. We haven't introduced causal graphs yet, but for the moment, it is sufficient to understand these graphs as intuitive maps of the data generating mechanism. In reality, they are causal DAGs, which we will introduce in the next chapter:
In Graph 1, A is assigned first, then L is assigned by some random function with a deterministic component that depends only on A, then Y is assigned by some random function that depends only on L. In Graph 2, L is assigned first, then A and Y are assigned by two different random functions that each depend only on L.
No matter how many people you sample, you cannot tell the graphs apart, because any joint distribution of L, A and Y that is consistent with graph 1, could also have been generated by graph 2. Distinguishing between the two possible data generating mechanisms is therefore not a statistical problem. This is one reason why model selection algorithms (which rely only on the joint distribution of observed variables for input) are not valid for causal inference.
Because even a complete sample is insufficient to learn about causal effects, you need a priori causal information in order to do this. This prior causal information comes in the form of the assumption “the data came from a complicated randomized trial run by nature”. If you have reason to doubt this assumption, you should also doubt the conclusions
What do we mean by Causality?
The first step of causal inference is to translate the English language research question «What is the causal effect of treatment» into a precise, mathematical language. One possible such language is based on counterfactual variables. These counterfactual variables allow us to encode the concept of “what would have happened if, possibly contrary to fact, treatment had been given”.
We define one counterfactual variable called Ya=1 which represents the outcome in the person if he has treatment, and another counterfactual variable called Ya=0 which represents the outcome if he does not have treatment. Counterfactual variables such as Ya=0 are mathematical objects that represent part of the data generating mechanism: The variable tells us what value the mechanism would assign to Y, if A is set to 0. These variables are columns in an imagined dataset that we sometimes call “God’s Table”:
Let us start by making some points about this spreadsheet. First, note that the counterfactual variables are variables just like any other column in the spreadsheet. Therefore, we can use the same type of logic that we use for any other variables. Second, note that in our framework, counterfactual variables are pre-treatment variables: They are determined long before treatment is assigned. The effect of treatment is simply to determine whether we see Ya=0 or Ya=1 in this individual.
The most important point about God’s Table is that we cannot observe Ya=1 and Ya=0. We only observe the joint distribution of observed variables, which we can call the “Observed Table”:
The goal of causal inference is to learn about God’s Table using information from the observed table (in combination with a priori causal knowledge). In particular, we are going to be interested in learning about the distributions of Ya=1 and Ya=0, and in how they relate to each other.
The “Gold Standard” for estimating the causal effect, is to run a randomized controlled trial where we randomly assign the value of A. This study design works because you select one random subset of the study population where you observe Ya=0, and another random subset where you observe Ya=1. You therefore have unbiased information about the distribution of both Ya=0 and of Ya=1.
An important thing to point out at this stage is that it is not necessary to use an unbiased coin to assign treatment, as long as your use the same coin for everyone. For instance, the probability of being randomized to A=1 can be 2/3. You will still see randomly selected subsets of the distribution of both Ya=0 and Ya=1, you will just have a larger number of people where you see Ya=1. Usually, randomized trials use unbiased coins, but this is simply done because it increases the statistical power.
Also note that it is possible to run two different randomized controlled trials: One in men, and another in women. The first trial will give you an unbiased estimate of the effect in men, and the second trial will give you an unbiased estimate of the effect in women. If both trials used the same coin, you could think of them as really being one trial. However, if the two trials used different coins, and you pooled them into the same database, your analysis would have to account for the fact that in reality, there were two trials. If you don’t account for this, the results will be biased. This is called “confounding”. As long as you account for the fact that there really were two trials, you can still recover an estimate of the population average causal effect. This is called “Controlling for Confounding”.
In general, causal inference works by specifying a model that says the data came from a complex trial, ie, one where nature assigned a biased coin depending on the observed past. For such a trial, there will exist a valid way to recover the overall causal results, but it will require us to think carefully about what the correct analysis is.
Assumptions of Causal Inference
We will now go through in some more detail about why it is that randomized trials work, ie , the important aspects of this study design that allow us to infer causal relationships, or facts about God’s Table, using information about the joint distribution of observed variables.
We will start with an “observed table” and build towards “reconstructing” parts of God’s Table. To do this, we will need three assumptions: These are positivity, consistency and (conditional) exchangeability:
Positivity is the assumption that any individual has a positive probability of receiving all levels of treatment: Pr(A=a) > 0 for all levels of a. If positivity does not hold, you will not have any information about the distribution of Ya for that level of a, and will therefore not be able to make inferences about it.
We can check whether this assumption holds in the data, by checking whether there are people who are treated and people who are untreated. If we observe a stratum where no individuals are treated (or no individuals are untreated), this can be either due to chance (random violation of positivity) or because individuals with these covariates were deterministically never treated (structural violation of positivity). As we will see later, our models can handle random violations, but not structural violations.
In a randomized controlled trial, positivity holds because you will use a coin that has a positive probability of assigning people to either arm of the trial.
The next assumption we are going to make is that if an individual happens to have treatment (A=1), we will observe the counterfactual variable Ya=1 in this individual. This is the observed table after we make the consistency assumption:
Making the consistency assumption got us half the way to our goal. We now have a lot of information about Ya=1 and Ya=0. However, half of the data is still missing.
Although consistency seems obvious, it is an assumption, not something that is true by definition. We can expect the consistency assumption to hold if we have a well-defined intervention (ie, the intervention is a well-defined choice, not an attribute of the individual), and there is no causal interference (one individual’s outcome is not affected by whether another individual was treated).
Consistency may not hold if you have an intervention that is not well-defined: For example, imagine you are interested in the effect of obesity, but there are several ways to gain weight. When you measure Ya=1 in people who gained weighted, it will actually be a composite of multiple counterfactual variables: One for people who decided to stop exercising (let us call that Ya=1*) and another for people who decided that they really like cake (let us call that Ya=1#). Since you failed to specify whether you are interested in the effect of cake or the effect of lack of exercise, the construct Ya=1 is a composite without any meaning, and people will be unable to use your results to predict the consequences of their actions.
To complete the table, we require an additional assumption on the nature of the data. We call this assumption “Exchangeability”. One possible exchangeability assumption is “Ya=0 ∐ A and Ya=1 ∐ A”. This is the assumption that says “The data came from a randomized controlled trial”. If this assumption is true, you will observe a random subset of the distribution of Ya=0 in the group where A=0, and a random subset of the distribution of Ya=1 in the group where A=1.
Exchangeability is a statement about two variables being independent from each other. This means that having information about either one of the variables will not help you predict the value of the other. Sometimes, variables which are not independent are "conditionally independent". For example, it is possible that knowing somebody's race helps you predict whether they enjoy eating Hakarl, an Icelandic form of rotting fish. However, it is also possible that this is just a marker for whether they were born in the ethnically homogenous Iceland. In such a situation, it is possible that once you already know whether somebody is from Iceland, also knowing their race gives you no additional clues as to whether they will enjoy Hakarl. In this case, the variables "race" and "enjoying hakarl" are conditionally independent, given nationality.
The reason we care about conditional independence is that sometimes you may be unwilling to assume that marginal exchangeability Ya=1 ∐ A holds, but you are willing to assume conditional exchangeability Ya=1 ∐ A | L. In this example, let L be sex. The assumption then says that you can interpret the data as if it came from two different randomized controlled trials: One in men, and one in women. If that is the case, sex is a "confounder". (We will give a definition of confounding in Part 2 of this sequence. )
If the data came from two different randomized controlled trials, one possible approach is to analyze these trials separately. This is called “stratification”. Stratification gives you effect measures that are conditional on the confounders: You get one measure of the effect in men, and another in women. Unfortunately, in more complicated settings, stratification-based methods (including regression) are always biased. In those situations, it is necessary to focus the inference on the marginal distribution of Ya.
If marginal exchangeability holds (ie, if the data came from a marginally randomized trial), making inferences about the marginal distribution of Ya is easy: You can just estimate E[Ya] as E [Y|A=a].
However, if the data came from a conditionally randomized trial, we will need to think a little bit harder about how to say anything meaningful about E[Ya]. This process is the central idea of causal inference. We call it “identification”: The idea is to write an expression for the distribution of a counterfactual variable, purely in terms of observed variables. If we are able to do this, we have sufficient information to estimate causal effects just by looking at the relevant parts of the joint distribution of observed variables.
The simplest example of identification is standardization. As an example, we will show a simple proof:
Begin by using the law of total probability to factor out the confounder, in this case L:
· E(Ya) = Σ E(Ya|L= l) * Pr(L=l) (The summation sign is over l)
We do this because we know we need to introduce L behind the conditioning sign, in order to be able to use our exchangeability assumption in the next step: Then, because Ya ∐ A | L, we are allowed to introduce A=a behind the conditioning sign:
· E(Ya) = Σ E(Ya|A=a, L=l) * Pr(L=l)
Finally, use the consistency assumption: Because we are in the stratum where A=a in all individuals, we can replace Ya by Y
· E(Ya) = Σ E(Y|A=a, L=l) * Pr (L=l)
We now have an expression for the counterfactual in terms of quantities that can be observed in the real world, ie, in terms of the joint distribution of A, Y and L. In other words, we have linked the data generating mechanism with the joint distribution – we have “identified” E(Ya). We can therefore estimate E(Ya)
This identifying expression is valid if and only if L was the only confounder. If we had not observed sufficient variables to obtain conditional exchangeability, it would not be possible to identify the distribution of Ya : there would be intractable confounding.
Identification is the core concept of causal inference: It is what allows us to link the data generating mechanism to the joint distribution, to something that can be observed in the real world.
The difference between epidemiology and biostatistics
Many people see Epidemiology as «Applied Biostatistics». This is a misconception. In reality, epidemiology and biostatistics are completely different parts of the problem. To illustrate what is going on, consider this figure:
The data generating mechanism first creates a joint distribution of observed variables. Then, we sample from the joint distribution to obtain data. Biostatistics asks: If we have a sample, what can we learn about the joint distribution? Epidemiology asks: If we have all the information about the joint distribution , what can we learn about the data generating mechanism? This is a much harder problem, but it can still be analyzed with some rigor.
Epidemiology without Biostatistics is always impossible: It would not be possible to learn about the data generating mechanism without asking questions about the joint distribution. This usually involves sampling. Therefore, we will need good statistical estimators of the joint distribution.
Biostatistics without Epidemiology is usually pointless: The joint distribution of observed variables is simply not interesting in itself. You can make the claim that randomized trials is an example of biostatistics without epidemiology. However, the epidemiology is still there. It is just not necessary to think about it, because the epidemiologic part of the analysis is trivial
Note that the word “bias” means different things in Epidemiology and Biostatistics. In Biostatistics, “bias” is a property of a statistical estimator: We talk about whether ŷ is a biased estimator of E(Y |A). If an estimator is biased, it means that when you use data from a sample to make inferences about the joint distribution in the population the sample came from, there will be a systematic source of error.
In Epidemiology, “bias” means that you are estimating the wrong thing: Epidemiological bias is a question about whether E(Y|A) is a valid identification of E(Ya). If there is epidemiologic bias, it means that you estimated something in the joint distribution, but that this something does not answer the question you were interested in.
These are completely different concepts. Both are important and can lead to your estimates being wrong. It is possible for a statistically valid estimator to be biased in the epidemiologic sense, and vice versa. For your results to be valid, your estimator must be unbiased in both senses.
Applied Causal Inference for Empirical Research
This sequence is an introduction to basic causal inference. It was originally written as auxiliary notes for a course in Epidemiology, but it is relevant to almost any kind of applied statistical and empirical research, including econometrics, sociology, psychology, political science etc. I would not be surprised if you guys find a lot of errors, and I would be very grateful if you point them out in the comments. This will help me improve my course notes and potentially help me improve my understanding of the material.
For mathematically inclined readers, I recommend skipping this sequence and instead reading Pearl's book on Causality. There is also a lot of good material on causal graphs on Less Wrong itself. Also, note that my thesis advisor is writing a book that covers the same material in more detail, the first two parts are available for free at his website.
Pearl's book, Miguel's book and Eliezer's writings are all more rigorous and precise than my sequence. This is partly because I have a different goal: Pearl and Eliezer are writing for mathematicians and theorists who may be interested in contributing to the theory. Instead, I am writing for consumers of science who want to understand correlation studies from the perspective of a more rigorous epistemology.
I will use Epidemiological/Counterfactual notation rather than Pearl's notation. I apologize if this is confusing. These two approaches refer to the same mathematical objects, it is just a different notation. Whereas Pearl would use the "Do-Operator" E[Y|do(a)], I use counterfactual variables E[Ya]. Instead of using Pearl's "Do-Calculus" for identification, I use Robins' G-Formula, which will give the same results.
For all applications, I will use the letter "A" to represent "treatment" or "exposure" (the thing we want to estimate the effect of), Y to represent the outcome, L to represent any measured confounders, and U to represent any unmeasured confounders.
Outline of Sequence:
I hope to publish one post every week. I have rough drafts for the following eight sections, and will keep updating this outline with links as the sequence develops:
Part 0: Sequence Announcement / Introduction (This post)
Part 1: Basic Terminology and the Assumptions of Causal Inference
Part 2: Graphical Models
Part 3: Using Causal Graphs to Understand Bias
Part 4: Time-Dependent Exposures
Part 5: The G-Formula
Part 6: Inverse Probability Weighting
Part 7: G-Estimation of Structural Nested Models and Instrumental Variables
Part 8: Single World Intervention Graphs, Cross-World Counterfactuals and Mediation Analysis
Introduction: Why Causal Inference?
The goal of applied statistical research is almost always to learn about causal effects. However, causal inference from observational is hard, to the extent that it is usually not even possible without strong, almost heroic assumptions. Because of the inherent difficulty of the task, many old-school investigators were trained to avoid making causal claims. Words like “cause” and “effect” were banished from polite company, and the slogan “correlation does not imply causation” became an article of faith which, when said loudly enough, seemingly absolved the investigators from the sin of making causal claims.
However, readers were not fooled: They always understood that epidemiologic papers were making causal claims. Of course they were making causal claims; why else would anybody be interested in a paper about the correlation between two variables? For example, why would anybody want to know about the correlation between eating nuts and longevity, unless they were wondering if eating nuts would cause them to live longer?
When readers interpreted these papers causally, were they simply ignoring the caveats, drawing conclusions that were not intended by the authors? Of course they weren’t. The discussion sections of epidemiologic articles are full of “policy implications” and speculations about biological pathways that are completely contingent on interpreting the findings causally. Quite clearly, no matter how hard the investigators tried to deny it, they were making causal claims. However, they were using methodology that was not designed for causal questions, and did not have a clear language for reasoning about where the uncertainty about causal claims comes from.
This was not sustainable, and inevitably led to a crisis of confidence, which culminated when some high-profile randomized trials showed completely different results from the preceding observational studies. In one particular case, when the Women’s Health Initiative trial showed that post-menopausal hormone replacement therapy increases the risk of cardiovascular disease, the difference was so dramatic that many thought-leaders in clinical medicine completely abandoned the idea of inferring causal relationships from observational data.
It is important to recognize that the problem was not that the results were wrong. The problem was that there was uncertainty that was not taken seriously by the investigators. A rational person who wants to learn about the world will be willing to accept that studies have errors of margin, but only as long as the investigators make a good-faith effort to examine what the sources of error are, and as long as they communicate clearly about this uncertainty to their readers. Old-school epidemiology failed at this. We are not going to make the same mistake. Instead, we are going to develop a clear, precise language for reasoning about uncertainty and bias.
In this context, we are going to talk about two sources of uncertainty – “statistical” uncertainty and “epidemiological” uncertainty.
We are going to use the word “Statistics” to refer to the theory of how we can learn about correlations from limited samples. For statisticians, the primary source of uncertainty is sampling variability. Statisticians are very good at accounting for this type of uncertainty: Concepts such as “standard errors”, “p-values” and “confidence intervals” are all attempts at quantifying and communicating the extent of uncertainty that results from sampling variability.
The old school of epidemiology would tell you to stop after you had found the correlations and accounted for the sampling variability. They believed going further was impossible. However, correlations are simply not interesting. If you truly believed that correlations tell you nothing about causation, there would be no point in doing the study.
Therefore, we are going to use the terms “Epidemiology” or “Causal Inference” to refer to the next stage in the process: Learning about causation from correlations. This is a much harder problem, with many additional sources of uncertainty, including confounding and selection bias. However, recognizing that the problem is hard does not mean that you shouldn't try, it just means that you have to be careful. As we will see, it is possible to reason rigorously about whether correlation really does imply causation in your particular study: You will just need a precise language. The goal of this sequence is simply to give you such a language.
In order to teach you the logic of this language, we are going to make several controversial statements such as «The only way to estimate a causal effect is to run a randomized controlled trial» . You may not be willing to believe this at first, but in order to understand the logic of causal inference, it is necessary that you are at least willing to suspend your disbelief and accept it as true within the course.
It is important to note that we are not just saying this to try to convince you to give up on observational studies in favor of randomized controlled trials. We are making this point because understanding it is necessary in order to appreciate what it means to control for confounding: It is not possible to give a coherent meaning to the word “confounding” unless one is trying to determine whether it is reasonable to model the data as if it came from a complex randomized trial run by nature.
When we say that causal inference is hard, what we mean by this is not that it is difficult to learn the basics concepts of the theory. What we mean is that even if you fully understand everything that has ever been written about causal inference, it is going to be very hard to infer a causal relationship from observational data, and that there will always be uncertainty about the results. This is why this sequence is not going to be a workshop that teaches you how to apply magic causal methodology. What we are interested in, is developing your ability to reason honestly about where uncertainty and bias comes from, so that you can communicate this to the readers of your studies. We want to teach you about, is the epistemology that underlies epidemiological and statistical research with observational data.
Insisting on only using randomized trials may seem attractive to a purist, it does not take much imagination to see that there are situations where it is important to predict the consequences of an action, but where it is not possible to run a trial. In such situations, there may be Bayesian evidence to be found in nature. This evidence comes in the form of correlations in observational data. When we are stuck with this type of evidence, it is important that we have a clear framework for assessing the strength of the evidence.
I am publishing Part 1 of the sequence at the same time as this introduction. I would be very interested in hearing feedback, particularly about whether people feel this has already been covered in sufficient detail on Less Wrong. If there is no demand, there won't really be any point in transforming the rest of my course notes to a Less Wrong format.
Thanks to everyone who had a look at this before I published, including paper-machine and Vika, Janos, Eloise and Sam from the Boston Meetup group.
- (Continuity/Achimedean) This axiom (and acceptable weaker versions of it) is much more subtle that it seems; "No choice is infinity important" is what it seems to say, but " 'I could have been a contender' isn't good enough" is closer to what it does. Anyway, that's a discussion for another time.
Here I'll explain briefly what I mean by it. Let's drop that axiom, and see what could happen. First of all, we could have a utility function with non-standard real value. This allows some things to be infinitely more important than others. A simple illustration is lexicographical ordering; eg my utility function consists of the amount of euros I end up owning, with the amount of sex I get serving as a tie-breaker.
There is nothing wrong with such a function! First, because in practice it functions as a standard utility function (I'm unlikely to be able to indulge in sex in a way that has absolutely no costs or opportunity costs, so the amount of euros will always predominate). Secondly because, even if it does make a difference... it's still expected utility maximisation, just a non-standard version.
But worse things can happen if you drop the axiom. Consider this decision criteria: I will act so that, at some point, there will have been a chance of me becoming heavy-weight champion of the world. This is compatible with all the other vNM axioms, but is obviously not what we want as a decision criteria. In the real world, such decision criteria is vacuous (there is a non-zero chance of me becoming heavyweight champion of the world right now), but it certainly could apply in many toy models.
That's why I said that the continuity axiom is protecting us from "I could have been a contender (and that's all that matters)" type reasoning, not so much from "some things are infinitely important (compared to others)".
Also notice that the quantum many-worlds version of the above decision criteria - "I will act so that the measure of type X universe is non-zero" - does not sound quite as stupid, especially if you bring in anthropics.
Crossposted from the Global Priorities Project
This is the first in a series of posts which take aim at the question: how should we prioritise work on problems where we have very little idea of our chances of success. In this post we’ll see some simple models-from-ignorance which allow us to produce some estimates of the chances of success from extra work. In later posts we’ll examine the counterfactuals to estimate the value of the work. For those who prefer a different medium, I gave a talk on this topic at the Good Done Right conference in Oxford this July.
How hard is it to build an economically efficient fusion reactor? How hard is it to prove or disprove the Goldbach conjecture? How hard is it to produce a machine superintelligence? How hard is it to write down a concrete description of our values?
These are all hard problems, but we don’t even have a good idea of just how hard they are, even to an order of magnitude. This is in contrast to a problem like giving a laptop to every child, where we know that it’s hard but we could produce a fairly good estimate of how much resources it would take.
Since we need to make choices about how to prioritise between work on different problems, this is clearly an important issue. We can prioritise using benefit-cost analysis, choosing the projects with the highest ratio of future benefits to present costs. When we don’t know how hard a problem is, though, our ignorance makes the size of the costs unclear, and so the analysis is harder to perform. Since we make decisions anyway, we are implicitly making some judgements about when work on these projects is worthwhile, but we may be making mistakes.
In this article, we’ll explore practical epistemology for dealing with these problems of unknown difficulty.
We will use a simplifying model for problems: that they have a critical threshold D such that the problem will be completely solved when D resources are expended, and not at all before that. We refer to this as the difficulty of the problem. After the fact the graph of success with resources will look something like this:
Of course the assumption is that we don’t know D. So our uncertainty about where the threshold is will smooth out the curve in expectation. Our expectation beforehand for success with resources will end up looking something like this:
Assuming a fixed difficulty is a simplification, since of course resources are not all homogenous, and we may get lucky or unlucky. I believe that this is a reasonable simplification, and that taking these considerations into account would not change our expectations by much, but I plan to explore this more carefully in a future post.
What kind of problems are we looking at?
We’re interested in one-off problems where we have a lot of uncertainty about the difficulty. That is, the kind of problem we only need to solve once (answering a question a first time can be Herculean; answering it a second time is trivial), and which may not easily be placed in a reference class with other tasks of similar difficulty. Knowledge problems, as in research, are a central example: they boil down to finding the answer to a question. The category might also include trying to effect some systemic change (for example by political lobbying).
This is in contrast to engineering problems which can be reduced down, roughly, to performing a known task many times. Then we get a fairly good picture of how the problem scales. Note that this includes some knowledge work: the “known task” may actually be different each time. For example, proofreading two pages of text is quite the same, but we have a fairly good reference class so we can estimate moderately well the difficulty of proofreading a page of text, and quite well the difficulty of proofreading a 100,000-word book (where the length helps to smooth out the variance in estimates of individual pages).
Some knowledge questions can naturally be broken up into smaller sub-questions. However these typically won’t be a tight enough class that we can use this to estimate the difficulty of the overall problem from the difficult of the first few sub-questions. It may well be that one of the sub-questions carries essentially all of the difficulty, so making progress on the others is only a very small help.
Model from extreme ignorance
One approach to estimating the difficulty of a problem is to assume that we understand essentially nothing about it. If we are completely ignorant, we have no information about the scale of the difficulty, so we want a scale-free prior. This determines that the prior obeys a power law. Then, we update on the amount of resources we have already expended on the problem without success. Our posterior probability distribution for how many resources are required to solve the problem will then be a Pareto distribution. (Fallenstein and Mennen proposed this model for the difficulty of the problem of making a general-purpose artificial intelligence.)
There is still a question about the shape parameter of the Pareto distribution, which governs how thick the tail is. It is hard to see how to infer this from a priori reasons, but we might hope to estimate it by generalising from a very broad class of problems people have successfully solved in the past.
This idealised case is a good starting point, but in actual cases, our estimate may be wider or narrower than this. Narrower if either we have some idea of a reasonable (if very approximate) reference class for the problem, or we have some idea of the rate of progress made towards the solution. For example, assuming a Pareto distribution implies that there’s always a nontrivial chance of solving the problem at any minute, and we may be confident that we are not that close to solving it. Broader because a Pareto distribution implies that the problem is certainly solvable, and some problems will turn out to be impossible.
This might lead people to criticise the idea of using a Pareto distribution. If they have enough extra information that they don’t think their beliefs represent a Pareto distribution, can we still say anything sensible?
Reasoning about broader classes of model
In the previous section, we looked at a very specific and explicit model. Now we take a step back. We assume that people will have complicated enough priors and enough minor sources of evidence that it will in practice be impossible to write down a true distribution for their beliefs. Instead we will reason about some properties that this true distribution should have.
The cases we are interested in are cases where we do not have a good idea of the order of magnitude of the difficulty of a task. This is an imprecise condition, but we might think of it as meaning something like:
There is no difficulty X such that we believe the probability of D lying between X and 10X is more than 30%.
Here the “30%” figure can be adjusted up for a less stringent requirement of uncertainty, or down for a more stringent one.
Now consider what our subjective probability distribution might look like, where difficulty lies on a logarithmic scale. Our high level of uncertainty will smooth things out, so it is likely to be a reasonably smooth curve. Unless we have specific distinct ideas for how the task is likely to be completed, this curve will probably be unimodal. Finally, since we are unsure even of the order of magnitude, the curve cannot be too tight on the log scale.
Note that this should be our prior subjective probability distribution: we are gauging how hard we would have thought it was before embarking on the project. We’ll discuss below how to update this in the light of information gained by working on it.
The distribution might look something like this:
In some cases it is probably worth trying to construct an explicit approximation of this curve. However, this could be quite labour-intensive, and we usually have uncertainty even about our uncertainty, so we will not be entirely confident with what we end up with.
Instead, we could ask what properties tend to hold for this kind of probability distribution. For example, one well-known phenomenon which is roughly true of these distributions but not all probability distributions is Benford’s law.
Approximating as locally log-uniform
It would sometimes be useful to be able to make a simple analytically tractable approximation to the curve. This could be faster to produce, and easily used in a wider range of further analyses than an explicit attempt to model the curve exactly.
As a candidate for this role, we propose working with the assumption that the distribution is locally flat. This corresponds to being log-uniform. The smoothness assumptions we made should mean that our curve is nowhere too far from flat. Moreover, it is a very easy assumption to work with, since it means that the expected returns scale logarithmically with the resources put in: in expectation, a doubling of the resources is equally good regardless of the starting point.
It is, unfortunately, never exactly true. Although our curves may be approximately flat, they cannot be everywhere flat -- this can’t even give a probability distribution! But it may work reasonably as a model of local behaviour. If we want to turn it into a probability distribution, we can do this by estimating the plausible ranges of D and assuming it is uniform across this scale. In our example we would be approximating the blue curve by something like this red box:
Obviously in the example the red box is not a fantastic approximation. But nor is it a terrible one. Over the central range, it is never out from the true value by much more than a factor of 2. While crude, this could still represent a substantial improvement on the current state of some of our estimates. A big advantage is that it is easily analytically tractable, so it will be quick to work with. In the rest of this post we’ll explore the consequences of this assumption.
Places this might fail
In some circumstances, we might expect high uncertainty over difficulty without everywhere having local log-returns. A key example is if we have bounds on the difficulty at one or both ends.
For example, if we are interested in X, which comprises a task of radically unknown difficulty plus a repetitive and predictable part of difficulty 1000, then our distribution of beliefs of the difficulty about X will only include values above 1000, and may be quite clustered there (so not even approximately logarithmic returns). The behaviour in the positive tail might still be roughly logarithmic.
In the other direction, we may know that there is a slow and repetitive way to achieve X, with difficulty 100,000. We are unsure whether there could be a quicker way. In this case our distribution will be uncertain over difficulties up to around 100,000, then have a spike. This will give the reverse behaviour, with roughly logarithmic expected returns in the negative tail, and a different behaviour around the spike at the upper end of the distribution.
In some sense each of these is diverging from the idea that we are very ignorant about the difficulty of the problem, but it may be useful to see how the conclusions vary with the assumptions.
Implications for expected returns
What does this model tell us about the expected returns from putting resources into trying to solve the problem?
Under the assumption that the prior is locally log-uniform, the full value is realised over the width of the box in the diagram. This is w = log(y) - log(x), where x is the value at the start of the box (where the problem could first be plausibly solved), y is the value at the end of the box, and our logarithms are natural. Since it’s a probability distribution, the height of the box is 1/w.
For any z between x and y, the modelled chance of success from investing z resources is equal to the fraction of the box which has been covered by that point. That is:
(1) Chance of success before reaching z resources = log(z/x)/log(y/x).
So while we are in the relevant range, the chance of success is equal for any doubling of the total resources. We could say that we expect logarithmic returns on investing resources.
Sometimes of greater relevance to our decisions is the marginal chance of success from adding an extra unit of resources at z. This is given by the derivative of Equation (1):
(2) Chance of success from a marginal unit of resource at z = 1/zw.
So far, we’ve just been looking at estimating the prior probabilities -- before we start work on the problem. Of course when we start work we generally get more information. In particular, if we would have been able to recognise success, and we have invested z resources without observing success, then we learn that the difficulty is at least z. We must update our probability distribution to account for this. In some cases we will have relatively little information beyond the fact that we haven’t succeeded yet. In that case the update will just be to curtail the distribution to the left of z and renormalise, looking roughly like this:
Again the blue curve represents our true subjective probability distribution, and the red box represents a simple model approximating this. Now the simple model gives slightly higher estimated chance of success from an extra marginal unit of resources:
(3) Chance of success from an extra unit of resources after z = 1/(z*(ln(y)-ln(z))).
Of course in practice we often will update more. Even if we don’t have a good idea of how hard fusion is, we can reasonably assign close to zero probability that an extra $100 today will solve the problem today, because we can see enough to know that the solution won’t be found imminently. This looks like it might present problems for this approach. However, the truly decision-relevant question is about the counterfactual impact of extra resource investment. The region where we can see little chance of success has a much smaller effect on that calculation, which we discuss below.
Comparison with returns from a Pareto distribution
We mentioned that one natural model of such a process is as a Pareto distribution. If we have a Pareto distribution with shape parameter α, and we have so far invested z resources without success, then we get:
(4) Chance of success from an extra unit of resources = α/z.
This is broadly in line with equation (3). In both cases the key term is a factor of 1/z. In each case there is also an additional factor, representing roughly how hard the problem is. In the case of the log-linear box, this depends on estimating an upper bound for the difficulty of the problem; in the case of the Pareto distribution it is handled by the shape parameter. It may be easier to introspect and extract a sensible estimate for the width of the box than for the shape parameter, since it is couched more in terms that we naturally understand.
In this post, we’ve just explored a simple model for the basic question of how likely success is at various stages. Of course it should not be used blindly, as you may often have more information than is incorporated into the model, but it represents a starting point if you don't know where to begin, and it gives us something explicit which we can discuss, critique, and refine.
In future posts, I plan to:
- Explore what happens in a field of related problems (such as a research field), and explain why we might expect to see logarithmic returns ex post as well as ex ante.
- Look at some examples of this behaviour in the real world.
- Examine the counterfactual impact of investing resources working on these problems, since this is the standard we should be using to prioritise.
- Apply the framework to some questions of interest, with worked proof-of-concept calculations.
- Consider what happens if we relax some of the assumptions or take different models.
I live in the UK, which has a very similar voting structure to the US for the purposes of this article. Nevertheless, it may differ on the details, for which I am sorry. I also use a couple of real-life political examples which I hope are uncontroversial enough not to break the unofficial rules here. If they are not, I can change them, because this is a discussion of gaming democracy by exploiting swing seats to push rationalist causes.
Cory Doctrow writes in the Guardian about using Kickstarter-like thresholds to encourage voting for minority parties:
He points out that nobody votes for minority parties because nobody else votes for them; if you waste your vote on Yellow then it is one fewer vote that might stop the hated Blue candidate getting in by voting for the not-quite-so-bad Green. He argues that you could use the internet to inform people when some pre-set threshold had been triggered with respect to voting for a minor party and thus encourage them to get out and vote. So for example if the margin of victory was 8000 votes and 9000 people agreed with the statement, “If more than 8000 people agree to this statement, then I will go to the polls on election day and vote for the minority Yellow party”, the minority Yellow party would win power even though none of the original 9000 participants would have voted for Yellow without the information-coordinating properties of the internet.
I’m not completely sure of the argument, but I looked into some of the numbers myself. There are 23 UK seats (roughly equivalent to Congressional Districts for US readers) with a margin of 500 votes or fewer. So to hold the balance of power in these seats you need to find either 500 non-voters who would be prepared to vote the way you tell them, or 250 voters with the same caveats (voters are worth twice as much as non-voters to the aspiring seat-swinger, since a vote taken from the Blues lowers the margin by one, and a vote given to the Greens lowers the margin by one, and every voter is entitled to both take a vote away from the party they are currently voting for and award a vote to any party of their choice). I’ll call the number of votes required to swing a seat the ‘effective voter’ count, which allows for the fact that some voters count for two.
It doesn’t sound impossible to me to reach the effective voter count for some swing constituencies, given that often even extremely obvious parody parties can often win back their deposit (500 actual votes, not even ‘effective votes’).
Doctrow wants to use the information co-ordination system to help minority parties reach a wider audience. I think it could be used in a much more active way to force policy promises on uncontroversial but low-status issues from potential future MPs. Let me take as an example ‘Research funding for transhuman causes’. Most people don’t know what transhumanism is, and most people who do know what it is don’t care. Most people who know what it is and care are basically in support of research into transhuman augmentations, but would definitely rank issues like the economy or defence as more important. There is a small constituency of people who oppose transhumanism outright, but they are not single issue voters either by any means (I imagine opposing transhumanism is strongly correlated with a ‘traditional religious value’ cluster which includes opposing abortion, gay marriage and immigration). Politicians could therefore (almost) costlessly support a small amount of research funding for transhuman, which would almost certainly be a sensible move when averaged across the whole country (either you discover something cool, in which case your population is made better off and your army more powerful or you don’t, and in the worst case you get a decent multiplier effect to the economy that comes from employing a load of material scientists and bioengineers). However we know that they won’t do this because while the benefits to the country might be great, the minor cost of supporting a low-status (‘weird’) project is borne entirely by the individual politician. What I mean by this is that the politician will probably not lose any votes by publically supporting transhumanism, but will lose status among their peers and will want to avoid this. There’s also a small risk of losing votes by supporting transhuman causes from the ‘traditional value’ cluster and no obvious demographic with whom supporting transhuman causes gains votes.
This indicates to me that if enough pro-transhumans successfully co-ordinated their action, they could bargain with the politicians standing for office. Let us say there are unequivocally enough transhumans to meet the effective voter threshold for a particular constituency. One person could go round each transhuman (maybe on that city’s subreddit) and get them to agree in principle to vote for whichever candidate will agree to always vote ‘Yes’ on research funding for transhuman causes, up to a maximum of £1bn. Each transhuman might have a weak preference for Blues vs Greens or vice versa, but the appeal is made to their sense of logic; each Blue vote is cancelled out by each Green vote, but each ‘Transhuman’ vote is a step closer to getting transhumanism properly funded, and transhumanism is more important than any marginal policy difference between the two parties. You then go to each candidate and present the evidence that the ‘transhuman’ block has the power to swing the election and is well co-ordinated enough to vote as a bloc on election day. If both candidates agree that they will vote ‘Yes’ on the bills you decided on, then send round an electronic message saying – essentially – “Vote your conscience”. If one candidate says ‘Yes’ and the other ‘No’ send round a message saying “Vote Blue” (or Green). If both candidates say ‘no’ send a message saying “Vote for the Transhuman Party (which is me)” in the hope that you can demonstrate you really did hold the balance of power, to increase the weight of your negotiation in the future.
If the candidate then goes back on their word, you slash and burn the constituency and make sure that no matter what the next candidate from that party promises, they lose. Also ensure that if that candidate ever stands in a marginal seat again, they lose (effectively ending their political career). This gives a strong incentive for MPs to vote the way they promised, and for parties to allow them to vote the way they promised.
Incidentally my preferred promise to extract from the candidates (and I don’t think this works in America) is to bring a bill with a particular wording if they win a Private Members’ Ballot (a system whereby junior members enter a lottery to see whose idea for a bill gets a ‘reading’ in the House of Commons, and hence a chance of becoming a law). For example, “This house would fund £1bn worth of transhumanism basic research over the next four years”. This is because it forces MPs to take a position on an issue they otherwise would not want to touch (because it is low-status) and one way out of this bind is to pretend the issue was high-status all along, which would be a good outcome for transhumanism as it means people might start funding it without the complicated information-coordination game I describe above.
One issue with this is that some groups – for example; Eurosceptics – are happy to single issue vote already, and there are far more Eurosceptics than there are rationalists in the UK. A US equivalent – as far as I understand – might be gun rights activists; they will vote for whatever party deregulates guns furthest, regardless of any other policies they might have and they are very numerous. This could be a problem, since a more numerous coalition will always beat a less numerous coalition at playing this information coordination game.
The first response is that it might actually be OK if this occurs. Being a Eurosceptic in no way implies a particular position on transhuman issues, so a politician could agree to the demands of the Eurosceptic bloc and transhuman bloc without issue. The numbers problem only occurs if a particular position automatically implies a position on another issue, so if there was a large single-issue anti-transhuman voting bloc, and there isn’t. There is a small problem if someone is both a Eurosceptic and a transhuman, since you can only categorically agree to vote the way one bloc tells you, but this is a personal issue where you have to decide which issue is more important and not a problem with the system as it stands.
The second response is that you are underestimating the difficulty of co-ordinating a vote in this way. For example, Eurosceptics – as a rule – will want to vote for the minority UKIP party to signal their affiliation with Eurosceptic issues. No matter what position the candidates agree to on Europe, UKIP will always be more extreme on European issues, since the candidate can only agree to sufficiently mainstream policies that the vote-cost of agreeing to the policy publically is less than the vote-gain of gaining the Eurosceptic bloc. Therefore there will be considerable temptation to defect and vote UKIP in the event of successfully coordinating a policy pledge from a candidate since the voter has a strong preference for UKIP over any other party. Transhumans – it is hypothesised – have a stronger preference for marginal gains in transhuman funding over any policy difference between the two major parties and so getting them to ‘hold their nose’ and vote for a candidate they would otherwise not want to is easier.
It is not just transhumanism that this vote-bloc scheme might work for, but transhumanism is certainly a good example. In my mind you could co-ordinate any issue where the proposed voting bloc is:
- Intelligent enough to understand why voting for a candidate you don’t like might result in outcomes you do like
- Sufficiently politically unaffiliated that voting for a party they disapprove of is a realistic prospect (hence I’m picking issues young people care about, since they typically don’t vote)
- Sufficiently internet-savvy that coordinating by email / reddit is a realistic prospect.
- Unopposed by any similar-sized or larger group which fits the above three criteria.
- Cares more about this particular issue than any other issue which fits the above four criteria
Some other good examples of this might be opposing homeopathy on the NHS, encouraging Effective Altruism in government foreign aid, spending a small portion of the Defence budget on FAI and so on.
Are there any glaring flaws I’ve missed?
Tentative tips for people engaged in an exercise that involves some form of prediction or forecasting
Note: This is the concluding post of my LessWrong posts related to my forecasting work for MIRI. There are a few items related to forecasting that I didn't get time to look into and might return to later. I might edit this post to include references to those posts if I get to them later.
I've been looking at forecasting in different domains as part of work for the Machine Intelligence Research Institute (MIRI). I thought I'd draw on whatever I've learned to write up advice for people engaged in any activity that involves making forecasts. This could include a wide range of activities, including those that rely on improving the accuracy of predictions in highly circumscribed contexts (such as price forecasting or energy use forecasting) as well as those that rely on trying to determine the broad qualitative contours of possible scenarios.
The particular application of interest to MIRI is forecasting AI progress, leading up to (but not exclusively focused on) the arrival of AGI. I will therefore try to link my general tips with thoughts on how it applies to forecasting AI progress. That being said, I hope that what I say here will have wider interest and appeal.
If you're interested in understanding the state of the art with respect to forecasting AI progress specifically, consider reading Luke Muehlhauser's summary of the state of knowledge on when AI will be created. The post was written in May 2013, and there have been a couple of developments since then, including:
- A paper by Vincent C. Müller and Nick Bostrom that describes a poll of artificial intelligence experts on future progress in the area
- An update by Paul Christiano and Katja Grace to the data collected in the paper by Stuart Armstrong and Kaj Sotala on how we're predicting AI (or failing to)
#1: Appreciate that forecasting is hard
It's hard to make predictions, especially about the future (see also more quotes here). Forecasting is a difficult job along many dimensions. Apart from being difficult, it's also a job where feedback is far from immediate. This holds more true as the forecasting horizon becomes wider (for lists of failed predictions made in the past, see here and here). Fortunately, a fair amount has been discovered about forecasting in general, and you can learn from the experience of people trying to make forecasts in many different domains.
Philip Tetlock's work on expert political judgment, whose conclusions he described here, and that I discussed in my post on the historical evaluations of forecasting, shows that at least in the domain of political forecasting, experts often don't do a much better job than random guesses, and even the experts who do well rarely do better than simple trend extrapolation. Not only do experts fail to do well, they are also poorly calibrated as to the quality of forecasts.
Even in cases where experts are right about the median or modal scenario, they often fail to both estimate and communicate forecast uncertainty.
The point that forecasting is hard, and should be approached with humility, will be repeated throughout this post, in different contexts.
#2: Avoid the "not invented here" fallacy, and learn more about forecasting across a wide range of different domains
The not invented here fallacy refers to people's reluctance to use tools developed outside of their domain or organization. In the context of forecasting, it's quite common. For instance, climate scientists have been accused of not following forecasting principles. The reaction of some of them has been along the lines of "why should we listen to forecasters, when they don't understand any climate science?" (more discussion of that response here, see also a similar answer on Quora). Moreover, it's not enough to only listen to outsiders who treat you with respect. The point of listening to and learning from other domains isn't to be generous to people in those domains, but to understand and improve one's own work (in this case, forecasting work).
There are some examples of successful importation of forecasting approaches from one domain to another. One example is the ideas developed for forecasting rare events, as I discussed in this post. Power laws for some rare phenomena, such as earthquakes, have been around for a while. Aaron Clauset and his co-authors have recently applied the same mathematical framework of power laws to other types of rare events, including terrorist attacks.
Evaluating AI progress forecasting on this dimension: My rough impression is that AI progress forecasting tends to be insular, learning little from other domains. While I haven't seen a clear justification from AI progress forecasters, the typical arguments I've seen are the historical robustness of Moore's law and the idea that the world of technology is fundamentally different from the world of physical stuff.
I think that future work on AI progress forecasting should explicitly consider forecasting problems in domains other than computing, and explicitly explain what lessons cross-apply and what don't, and why. I don't mean that all future work should consider all other domains. I just mean that at least some future work should consider at least some other domains.
#3: Start by reading a few really good general-purpose overviews
Personally, I would highlight Nate Silver's The Signal and the Noise. Silver's book is quite exceptional in the breadth of topics it covers, the clarity of its presentation, and the easy toggling between general principles and specific instances. Silver's book comfortably combines ideas from statistics, data mining, machine learning, predictive analytics, and forecasting. Not only would I recommend reading it quickly when you're starting out, I would also recommend returning to specific chapters of the book later if they cover topics that interest you. I personally found the book a handy reference (and quoted extensively from it) when writing LessWrong posts about forecasting domains that the book has covered.
Other books commonly cited are Tetlock's Expert Political Judgment and the volume Principles of Forecasting edited by J. Scott Armstrong, and contributed to by several forecasters. I believe both these books are good, but I'll be honest: I haven't read them, although I have read summaries of the books and shorter works by the authors describing the main points. I believe that you can similarly get the bulk of the value of Tetlock's work by reading his article for Cato Unbound co-authored with Dan Gardner, that I discussed here. For the principles of forecasting, see #4 below.
Evaluating AI progress forecasting on this dimension: There seems to be a lot of focus on a few AI-related and computing-related futurists, such as Ray Kurzweil. I do think the focus should be widened, and getting an understanding of general challenges related to forecasting is a better starting point than reading The Singularity is Near. That said, the level of awareness among MIRI and LessWrong people about the work of Silver, Armstrong, and Tetlock definitely seems higher than among the general public or even among the intelligentsia. I should also note that Luke Muehlhauser was the person who first pointed me to J. Scott Armstrong, and he's referenced Tetlock's work frequently.
#4: Understand key concepts and distinctions in forecasting, and review the literature and guidelines developed by the general-purpose forecasting community
In this post, I provided an overview of different kinds of forecasting, and also included names of key people, key organizations, key journals, and important websites. I would recommend reading that to get a general sense, and then proceeding to the Forecasting Principles website (though, fair warning: the website's content management system is a mess, and in particular, you might find a lot of broken links). Here's their full list of 140 principles, along with discussion of the evidence base for each principle. However, see also point #5 below.
#5: Understand some alternatives to forecasting, specifically scenario analysis and futures studies
If you read the literature commonly classified as "forecasting" in academia, you will find very little mention of scenario analysis and futures studies. Conversely, the literature on scenario analysis and futures studies rarely cites the general-purpose forecasting literature. But the actual "forecasting" exercise you intend to engage in may be better suited to scenario analysis than to forecasting. Or you might find that the methods of futures studies are a closer fit for what you are trying to achieve. Or you might try to use a mix of techniques.
Broadly, scenario analysis becomes more important when there is more uncertainty, and when it's important to be prepared for a wider range of eventualities. This matters more as we move to longer time horizons for forecasting. I discussed scenario analysis in this post, where I also speculate on possible reasons for the lack of overlap with the forecasting community.
Futures studies is closely related to scenario analysis (in fact, scenario analysis can be considered a method of futures studies) but the futures studies field has a slightly different flavor. I looked at the field of futures studies in this post.
It could very well be the case that you find the ideas of scenario analysis and futures studies inappropriate for the task at hand. But such a decision should be made only after acquiring a reasonable understanding of the methods.
Some other domains that might be better suited to the problem at hand include predictive analytics, predictive modeling, data mining, machine learning, and risk analysis. I haven't looked into any of these in depth in connection with my MIRI project (I've been reading up on machine learning for other work, and have been and will be posting about it on LessWrong but that's independent of my MIRI work).
Evaluating AI progress forecasting on this dimension: I think a reasonable case can be made that the main goals of AI progress forecasting are better met through scenario analysis. I discussed this in detail in this post.
#6: Examine forecasting in other domains, including domains that do not seem to be related to your domain at the object level
This can be thought of as a corollary to #2. Chances are, if you have read Nate Silver and some of the other sources, your curiosity about forecasting in other domains has already been piqued. General lessons about human failure and error may cross-apply between domains, even if the object-level considerations are quite different.
In addition to Silver's book, I recommend taking a look at some of my own posts on forecasting in various domains. These posts are based on rather superficial research, so please treat them only as starting points.
Some domain-specific posts:
- Track record of survey-basedmacroeconomic forecasting
- Lessons from weather forecasting and its history for forecasting as a domain and
- Weather and climate forecasting: how the challenges differ by time horizon
- An overview of forecasting for politics, conflict, and political violence
- I've written about technology forecasting here, here (a look at Megamistakes), and here.
I also did some additional posts on climate science as a case study in forecasting. I have paused the exercise due to time and ability limitations, but I think the posts so far might be useful:
- Climate science: how it matters for understanding forecasting, materials I've read or plan to read, sources of potential bias
- Time series forecasting for global temperatures: an outside view of climate forecasting
- Carbon dioxide, climate sensitivity, feedbacks, and the historical record: a cursory examination of the Anthropogenic Global Warming (AGW) hypothesis
- [QUESTION]: What are your views on climate science, and how did you form them?
- The insularity critique of climate science
#7: Consider setting up data collection using best practices early on
Forecasting works best when we have a long time series of data to learn from. So it's best to set up data collection as quickly as possible, and use good practices in setting it up. Data about the present or recent past may be cheap to collect now, but could be hard to collect a few decades from now. We don't want to be spending our time two decades later figuring out how to collect data (and adjudicating disputes about the accuracy of data) if we could collect and archive the data in a stable repository right now.
If your organization is too small to do primary data collection, find another organization that engages in the data collection activities, and make sure you archive the data they collect, so that the data is available to you even if that organization stops operating.
Evaluating AI progress forecasting on this dimension: I think that there are some benefits from creating standardized records and measurements of the current state of AI and the quality of the current hardware and software. That said, there do exist plenty of reasonably standardized measurements already in these domains. There is little danger of this information completely disappearing, so that the project of combining and integrating them into a big picture is important but not time-sensitive. Hardware progress and specs are already well-documented, and we can get time series at places such as the Performance Curve Database. Software progress and algorithmic progress have also been reasonably well-recorded, as described by Katja Grace in her review for MIRI of algorithmic progress in six domains.
#8: Consider recording forecasts and scenarios, and the full reasoning or supporting materials
It's not just useful to have data from the past, it's also useful to have forecasts made based on past data and see how they compared to what actually transpired. The problem with forecasts is even worse than with data: if two decades later we want to know what one would have predicted using the data that is available right now, we simply cannot do that unless we make and record the predictions now. (We could do it in principle by imagining that we don't have access to the intermediate data. But in practice, people can find it hard to avoid being influenced by their knowledge of what has transpired in the interim when they build and tune their models). Retrodictions and hindcasts are useful for analysis and diagnosis, but they ultimately do not provide a convincing independent test of the model being used to make forecasts.
Evaluating AI progress forecasting on this dimension: See the link suggestions for recent work on AI progress forecasting at the beginning of the post.
The remaining points are less important and more tentative. I've included for completeness' sake.
#9: Evaluate how much expertise the domain experts have in forecasting
In some cases, domain experts also have expertise in making forecasts. In other cases, the relationship between domain expertise and the ability to make forecasts, or even to calibrate one's own forecast accuracy, is tenuous. I discussed the issue of how much deference to give to domain experts in this post.
#10: Use best practices from statistical analysis, computer programming, software engineering, and economics
Wherever using these disciplines, use them well. Statistical analysis arises in quantitative forecasting and prediction. Computer programming is necessary for setting up prediction markets or carrying out time series forecasting or machine learning with large data sets or computationally intensive algorithms. Software engineering is necessary once the computer programs exceed a basic level of complexity, or if they need to survive over the long term. Insights from economics and finance may be necessary for designing effective prediction markets or other tools to incentivize people to make accurate predictions and minimize their chances of gaming the system in ways detrimental to prediction accuracy.
The insularity critique of climate science basically accused the discipline of not doing this.
What if your project is too small and you don't have access to expertise in these domains? Often, a very cursory, crude analysis can be helpful in ballparking the situation. As I described in my historical evaluations of forecasting, the Makridakis Competitions provide evidence in favor of the hypothesis that simple models tend to perform quite well, although the correctly chosen complex models can outperform simple ones under special circumstances (see also here). So keeping it simple to begin with is fine. However, the following caveats should be noted:
- Even "simple" models and setups can benefit from overview by somebody with subject matter expertise. The overviews can be fairly quick, but they still help. For instance, after talking to a few social scientists, I realized the perils of using simple linear regression for time series data. This isn't a deep point, but it can elude even a smart and otherwise knowledgeable person who hasn't thought much about the specific tools.
- The limitations of the model, and the uncertainty in the associated forecast, should be clearly noted (see my post on communicating forecast uncertainty).
Evaluating AI progress forecasting on this dimension: I think that AI progress forecasting is at too early a stage to get into using detailed statistical analysis or software, so using simple models and getting feedback from experts, while noting potential weaknesses, seems like a good strategy.
#11: Consider carefully the questions of openness of data, practices, supporting code, and internal debate
While confidentiality and anonymity are valuable in some contexts, openness and transparency are good antidotes to errors that arise due to insufficient knowledge and groupthink (such as the types of problems I noted in my post on the insularity critique of climate science).
#12: Consider ethical issues related to forecasting, such as the waysyour forecasting exercise can influence real-world decisions and outcomes
This is a topic I intended to look into more but didn't get time to. I've collected a few links for interested parties:
- Political and ethical issues in forecasting
- The Role of Ethics in Statistical Forecasting
- Information for Practitioners, and Legal Aspects of Forecasting on the Forecasting Principles website
If it's worth saying, but not worth its own post (even in Discussion), then it goes here.
Notes for future OT posters:
1. Please add the 'open_thread' tag.
2. Check if there is an active Open Thread before posting a new one.
3. Open Threads should be posted in Discussion, and not Main.
4. Open Threads should start on Monday, and end on Sunday.
Still very much a work in progress
Why do we bother about utility functions on Less Wrong? Well, because of results of the New man and the Morning Star, which showed that, essentially, if you make decisions, you better use something equivalent to expected utility maximisation. If you don't, you lose. Lose what? It doesn't matter, money, resources, whatever: the point is that any other system can be exploited by other agents or the universe itself to force you into a pointless loss. A pointless loss being a lose that give you no benefit or possibility of benefit - it's really bad.
The justifications for the axioms of expected utility are, roughly:
- (Completeness) "If you don't decide, you'll probably lose pointlessly."
- (Transitivity) "If your choices form loops, people can make you lose pointlessly."
- (Continuity/Achimedean) This axiom (and acceptable weaker versions of it) is much more subtle that it seems; "No choice is infinity important" is what it seems to say, but " 'I could have been a contender' isn't good enough" is closer to what it does. Anyway, that's a discussion for another time.
- (Independence) "If your choice aren't independent, people can expect to make you lose pointlessly."
Equivalency is not identity
A lot of people believe a subtlety different version of the result:
- If you don't have a utility function, you'll lose pointlessly.
This is wrong. The correct result is:
- If you don't lose pointlessly, then your decisions are equivalent with having a utility function.
A look at all natural foods through the lenses of Bayesianism, optimisation, and friendly utility functions.
How should we consider foods that claim to be "all natural"? Or, since that claim is a cheap signal, foods that have few ingredients, all of them easy to recognise and all "natural"? Or "GM free"?
From the logical point of view, the case is clear: valuing these foods is nothing more that the appeal to nature fallacy. Natural products include many pernicious things (such as tobacco, hemlock, belladonna, countless parasites, etc...). And the difference between natural and not-natural isn't obvious: synthetic vitamin C is identical to the "natural" molecule, and gene modifications are just advanced forms of selective breeding.
But we're not just logicians, we're Bayesians. So let's make a few prior assumptions:
- There are far more possible products in the universe that are bad to eat than are good.
- Products that humans have been consuming for generations are much more likely to be good to eat that than a random product.
Now let's see the food industry as optimising along a few axis:
- Cost. This should be low.
- Immediate consumer satisfaction (including taste, appearance, texture, general well-being for a week or so). This should be high.
- Long term damage to the consumer's health. This should be low.
Summary: Is there demand for writing posts about this aspect of decision-making?
And of course, is there offer? Because I didn't see any post about it.
Topics I intended to cover include:
- How much is worth 100$ in few years? Why? Why is it useful?
- Risk-return relationship.
- How is it useful in life outside finance?
And topic I would like, but I am not sure if i should cover:
- How can we apply it to death? (in sense, should I live a happy life or struggle to live endlessly?)
I found that missing in decision analysis, and I think it is very important thing to know, since we don't always choose between "I take A" or "I take B", but also between "I take A" or "I take B in two years", or "should i give A to gain B every year next 100 years?"
Why not simply redirect to some other source?
Well, that can be done either way, but I thought clear basics would not harm and would be useful to people who want to invest less time in it.
[I'm unsure how much this rehashes things 'everyone knows already' - if old hat, feel free to downvote into oblivion. My other motivation for the cross-post is the hope it might catch the interest of someone with a stronger mathematical background who could make this line of argument more robust]
Many outcomes of interest have pretty good predictors. It seems that height correlates to performance in basketball (the average height in the NBA is around 6'7"). Faster serves in tennis improve one's likelihood of winning. IQ scores are known to predict a slew of factors, from income, to chance of being imprisoned, to lifespan.
What is interesting is the strength of these relationships appear to deteriorate as you advance far along the right tail. Although 6'7" is very tall, is lies within a couple of standard deviations of the median US adult male height - there are many thousands of US men taller than the average NBA player, yet are not in the NBA. Although elite tennis players have very fast serves, if you look at the players serving the fastest serves ever recorded, they aren't the very best players of their time. It is harder to look at the IQ case due to test ceilings, but again there seems to be some divergence near the top: the very highest earners tend to be very smart, but their intelligence is not in step with their income (their cognitive ability is around +3 to +4 SD above the mean, yet their wealth is much higher than this) (1).
The trend seems to be that although we know the predictors are correlated with the outcome, freakishly extreme outcomes do not go together with similarly freakishly extreme predictors. Why?
Too much of a good thing?
One candidate explanation would be that more isn't always better, and the correlations one gets looking at the whole population doesn't capture a reversal at the right tail. Maybe being taller at basketball is good up to a point, but being really tall leads to greater costs in terms of things like agility. Maybe although having a faster serve is better all things being equal, but focusing too heavily on one's serve counterproductively neglects other areas of one's game. Maybe a high IQ is good for earning money, but a stratospherically high IQ has an increased risk of productivity-reducing mental illness. Or something along those lines.
I would guess that these sorts of 'hidden trade-offs' are common. But, the 'divergence of tails' seems pretty ubiquitous (the tallest aren't the heaviest, the smartest parents don't have the smartest children, the fastest runners aren't the best footballers, etc. etc.), and it would be weird if there was always a 'too much of a good thing' story to be told for all of these associations. I think there is a more general explanation.
The simple graphical explanation
[Inspired by this essay from Grady Towers]
Suppose you make a scatter plot of two correlated variables. Here's one I grabbed off google, comparing the speed of a ball out of a baseball pitchers hand compared to its speed crossing crossing the plate:
It is unsurprising to see these are correlated (I'd guess the R-square is > 0.8). But if one looks at the extreme end of the graph, the very fastest balls out of the hand aren't the very fastest balls crossing the plate, and vice versa. This feature is general. Look at this data (again convenience sampled from googling 'scatter plot') of quiz time versus test score:
Given a correlation, the envelope of the distribution should form some sort of ellipse, narrower as the correlation goes stronger, and more circular as it gets weaker:
The thing is, as one approaches the far corners of this ellipse, we see 'divergence of the tails': as the ellipse doesn't sharpen to a point, there are bulges where the maximum x and y values lie with sub-maximal y and x values respectively:
So this offers an explanation why divergence at the tails is ubiquitous. Providing the sample size is largeish, and the correlation not to tight (the tighter the correlation, the larger the sample size required), one will observe the ellipses with the bulging sides of the distribution (2).
Hence the very best basketball players aren't the tallest (and vice versa), the very wealthiest not the smartest, and so on and so forth for any correlated X and Y. If X and Y are "Estimated effect size" and "Actual effect size", or "Performance at T", and "Performance at T+n", then you have a graphical display of winner's curse and regression to the mean.
An intuitive explanation of the graphical explanation
It would be nice to have an intuitive handle on why this happens, even if we can be convinced that it happens. Here's my offer towards an explanation:
The fact that a correlation is less than 1 implies that other things matter to an outcome of interest. Although being tall matters for being good at basketball, strength, agility, hand-eye-coordination matter as well (to name but a few). The same applies to other outcomes where multiple factors play a role: being smart helps in getting rich, but so does being hard working, being lucky, and so on.
For a toy model, pretend these height, strength, agility and hand-eye-coordination are independent of one another, gaussian, and additive towards the outcome of basketball ability with equal weight.(3) So, ceritus paribus, being taller will make one better at basketball, and the toy model stipulates there aren't 'hidden trade-offs': there's no negative correlation between height and the other attributes, even at the extremes. Yet the graphical explanation suggests we should still see divergence of the tails: the very tallest shouldn't be the very best.
The intuitive explanation would go like this: Start at the extreme tail - +4SD above the mean for height. Although their 'basketball-score' gets a massive boost from their height, we'd expect them to be average with respect to the other basketball relevant abilities (we've stipulated they're independent). Further, as this ultra-tall population is small, this population won't have a very high variance: with 10 people at +4SD, you wouldn't expect any of them to be +2SD in another factor like agility.
Move down the tail to slightly less extreme values - +3SD say. These people don't get such a boost to their basketball score for their height, but there should be a lot more of them (if 10 at +4SD, around 500 at +3SD), this means there is a lot more expected variance in the other basketball relevant activities - it is much less surprising to find someone +3SD in height and also +2SD in agility, and in the world where these things were equally important, they would 'beat' someone +4SD in height but average in the other attributes. Although a +4SD height person will likely be better than a given +3SD height person, the best of the +4SDs will not be as good as the best of the much larger number of +3SDs
The trade-off will vary depending on the exact weighting of the factors, which explain more of the variance, but the point seems to hold in the general case: when looking at a factor known to be predictive of an outcome, the largest outcome values will occur with sub-maximal factor values, as the larger population increases the chances of 'getting lucky' with the other factors:
So that's why the tails diverge.
Endnote: EA relevance
I think this is interesting in and of itself, but it has relevance to Effective Altruism, given it generally focuses on the right tail of various things (What are the most effective charities? What is the best career? etc.) It generally vindicates worries about regression to the mean or winner's curse, and suggests that these will be pretty insoluble in all cases where the populations are large: even if you have really good means of assessing the best charities or the best careers so that your assessments correlate really strongly with what ones actually are the best, the very best ones you identify are unlikely to be actually the very best, as the tails will diverge.
This probably has limited practical relevance. Although you might expect that one of the 'not estimated as the very best' charities is in fact better than your estimated-to-be-best charity, you don't know which one, and your best bet remains your estimate (in the same way - at least in the toy model above - you should bet a 6'11" person is better at basketball than someone who is 6'4".)
There may be spread betting or portfolio scenarios where this factor comes into play - perhaps instead of funding AMF to diminishing returns when its marginal effectiveness dips below charity #2, we should be willing to spread funds sooner.(4) Mainly, though, it should lead us to be less self-confident.
1. One might look at the generally modest achievements of people in high-IQ societies as further evidence, but there are worries about adverse selection.
2. One needs a large enough sample to 'fill in' the elliptical population density envelope, and the tighter the correlation, the larger the sample needed to fill in the sub-maximal bulges. The old faithful case is an example where actually you do get a 'point', although it is likely an outlier.
3. If you want to apply it to cases where the factors are positively correlated - which they often are - just use the components of the other factors that are independent of the factor of interest. I think, but I can't demonstrate, the other stipulations could also be relaxed.
4. I'd intuit, but again I can't demonstrate, the case for this becomes stronger with highly skewed interventions where almost all the impact is focused in relatively low probability channels, like averting a very specified existential risk.
There is a site dedicated to the story at hpmor.com, which is now the place to go to find the authors notes and all sorts of other goodies. AdeleneDawner has kept an archive of Author’s Notes. (This goes up to the notes for chapter 76, and is now not updating. The authors notes from chapter 77 onwards are on hpmor.com.)Spoiler Warning: this thread is full of spoilers. With few exceptions, spoilers for MOR and canon are fair game to post, without warning or rot13. More specifically:
You do not need to rot13 anything about HP:MoR or the original Harry Potter series unless you are posting insider information from Eliezer Yudkowsky which is not supposed to be publicly available (which includes public statements by Eliezer that have been retracted).
If there is evidence for X in MOR and/or canon then it’s fine to post about X without rot13, even if you also have heard privately from Eliezer that X is true. But you should not post that “Eliezer said X is true” unless you use rot13.
I have trouble expressing myself in such a way that my ideas come out even remotely like they sound in my head. So please apply the principle of charity and try to read how you think I thought of it.
Tit for Tat
Tit for Tat is usually presented in a game between two players where each chooses to either cooperate or defect. The real world game however differs in two important ways.
First, it's not a two player game. We make choices not only on our single instance of interaction but also on observed interactions between other players. Thus the Advanced Tit For Tat not only defects if the other player defected against itself but also if it could observe the other player defecting against any other player that employs a similar enough algorithm.
Second, there is a middle ground between cooperating and defecting, you could stay neutral. Thus you can harm your opponent, help him or do neither. The question of the best strategy in this real life prisoners dilemma is probably still unanswered. If I see my opponent defecting against some of my peers and cooperating with others, what do I choose?
The reason why there even is a game is because we can deliberate on our action and can take abstract thoughts into account that do not directly pertain to the current situation, which I think is the distinguishing factor of higher animals from lower. This ability is called agency. In order to be an agent a subject must be able to perceive the situation, have a set of possible actions, model the outcomes of these actions, value the outcomes, and then act accordingly.
We could act in such a way that infringes on these abilities in others. If we limit their ability to perceive or model the situation we call this fraud, if we limit their set of possible actions or their ability to choose between them, we call it coercion, if we infringe on their ability to value an outcome, we call it advertising.
I propose that the purpose of our moral or ethical intuitions (I use the two words interchangeably, if there is a distinction please let me know) is to tell us whether some player defected, cooperated or stayed neutral, and to tell us who we should consider as having a close enough decision algorithm to ourselves to 'punish' third players for defecting against them. And I further propose that infringing on someones agency is what we consider as defecting.
Utilitarians tend to see defecting or cooperating as pertaining to creation or destruction of values. (Edit:) Three things bother me about value ethics:
1. Valuations between different people can't really be compared. If we shut up and multiply, we value the lives of everybody exactly the same no matter how they themselves value their own life. If there are chores to be done and one person claims to "not mind too much" while the other claims to "hate it with a passion" we can't tell if the emotional effect on them is really any different or maybe even the other way round.
2. It makes you torture someone to avoid an insanely huge number of dust specs.
3. It makes you push a fat man to his death.
Instead I propose that defecting in the real world game is all about infringing on someone's agency. Thus we intuit bankers who destroy an insane amount of wealth while not as good people still as neutral because they do not infringe on agency. At least that is my moral intuition.
So infringing on agency would make you a bad person, while not infringing on agency doesn't make you a good person. What makes you a good person is increasing value. Maybe agency is more fundamental and you cannot be a good person if you are a bad person, but maybe you can be both. That would create cognitive dissonance in people who consider ethics to be a singular thing and don't see the distinction, and that might be at the root of some ethics discussions.
In my version of ethics it counts as evil to push the fat man or to switch the tracks, as that would mean deliberately causing a death of someone who doesn't want to die. I would let the five die and not feel guilty about it, because I am not the cause of their deaths. I make a fundamental distinction between acting and not acting. If I hadn't been there the five would still die, so how could I be responsible for their deaths? I am aware that this view makes me evil in the eye of utilitarians. But I see less people acting consistent with utilitarianism than I see people arguing that way. Then again, this perception is probably heavily biased.
I don't really have a conclusion except of noticing that there exists a disagreement in fundamental morality and to inform you that there exists at least one person who considers infringing on someone's agency as defecting in a prisoner's dilemma.
How much AI technique could it possibly take for google (or something better) to do a decent job with
speechby:obama attitude:positive "Saul Alinsky".
I.e. "speechby:" and "attitude:" don't exist, but could, I believe be implemented pretty accurately, to see in this case if we can find any instances of Obama praising Saul Alinsky.
An article: "Bill Ayers and Obama Both Quote Alinsky" claims such quotes exist, but their one attempt to demonstrate it is laughable -- something vaguely like a paraphrase of an Alinsky statement, but which has, in fact the reverse sense of what the supposed "original" meant. Yet I think most of the world, and not just conservatives, if they have any idea who Alinsky is, will tend not to question Obama's "debt" to Alinski -- just for the sheer number of times it's been said or implied. For the other shoe dropping, false quotes that help demonize Alinsky, see tinyurl.com/qa6fglk.
The point isn't to defend Obama. It is that I think the world would work better if the ratio of
ability to find verifiable facts pertinent to political discussion
supply of highly opinionated and slanted "news".
could be raised by, say, an order of magnitude.
So many assertions are made that are likely not true, but are incredibly difficult for the average person to disprove. In this Internet era, the personal cost to write some almost free associative screed about a political point is very low, while the personal cost of finding quite a lot of pertinent facts is awfully high.
This is not to say the "average person" will look for facts to confirm or contradict what they read, but much of what they read is written by bloggers some of whom are sincere and would become users of such resources, and I do believe the emotional rewards of finding a nugget of truth versus the current pain of often fruitless search would have an effect on people's thinking habits -- maybe small at first but growing over time.
The particular proposal merely illustrates one of many sorts of resource that are missing or hard to find. Ideas for other such resources would be welcome.
Green Martians and Blue Martians have one thing in common: They both derive a tremendous amount of utility from tickling humans behind the ears, using their soft, feathery tentacles. In fact, the utility that they derive from this is so intense that most scientists believe at some time in the recent evolutionary past, there must have been a large selection pressure directed at ensuring that Martians were motivated to tickle humans.
There are numerous differences between Green and Blue Martians. One of those differences is that whereas the feathery tentacles of Green Martians contain stinging hairs similar to nettles, the analogous anatomic part of the Blue Martian contains a safe drug with an euphoric effect. Therefore, humans who are tickled by green martians experience a moderate stinging pain, whereas those who are tickled by blue martians experience mild to moderate pleasure.
Human ethicists have long struggled to come up with a coherent ethical theory that determines whether tickling humans is morally acceptable. Some have suggested that tickling humans behind the ear is ethically permissible if and only if you are a blue martian. However, many other thinkers are worried that this line of thinking results in an unjust world, where the ethics of an act is determined by characteristics of the Martian that they cannot be held responsible for.
However, human ethicists are not very familiar with Martian physiology, and the situation is actually even more complicated than they suspect. In fact, all Martians are born Green. They can shed their green shell and become blue Martians only after they have perfected the art of tickling humans with their feathery tentacles. All Martians aspire to one day become blue, but the amount of practicing it takes to reach perfection is highly variable - some martians reach perfection at their first attempt, whereas others keep trying their whole life without making any discernible progress. Therefore, if the ethical code says that green martians are prohibited from tickling humans, ethical Martians will be unable to reach their full potential in life, and will be stuck as Green Martians forever. Under this ethical code, only unethical Martians will be able to metamorphose.
Making the situation even more complicated, is the fact that a group of recently metamorphosed Blue Martians are vocally spreading information on the internet about tickling techniques. These techniques are sometimes effective, but if used imperfectly they increase the sting of the stinging hairs fourfold. Importantly, it seems that part of the reason some young Green Martians are naturally better ticklers and therefore metamorphose earlier, is that they intuitively understand these techniques, and are able to apply them without increasing the sting of their tentacles. Moreover, while the tickling technique has empirical support, the theory behind it relies heavily on speculation about human evolutionary history that may not be true, and which is offensive to humans.
This raises a number of additional ethical questions: Is it unethical for a Green Martian to attempt to metamorphose? Does this depend on whether they believe themselves to be fast or slow learners? Should only the small subset of Martians who intuitively understand the tickling techniques be allowed to use them? Is spreading explicit information about the techniques unethical?
(Note : This parable is obviously an allegory for something. Discussing whether the allegory is valid is interesting, but will lead to mindkill. I would prefer if the discussion could stay focused on the Martians, so that we can discuss the ethics of a hypothetical scenario that may not be relevant in real life. I am genuinely confused about the ethics of this, and I think this can lead to an interesting question regardless of whether it is applicable to humans)
- [Atlanta] MIRIxAtlanta: 19 July 2014: 19 July 2014 06:00PM
- Frankfurt: Goal Factoring: 20 July 2014 02:00PM
- Houston, TX: 19 July 2014 12:16AM
- Upper Canada LW Megameetup: Ottawa, Toronto, Montreal, Waterloo, London: 18 July 2014 07:00PM
The remaining meetups take place in cities with regular scheduling, but involve a change in time or location, special meeting content, or simply a helpful reminder about the meetup:
- Brussels - August (topic TBD): 09 August 2014 01:00PM
- Canberra: Intro to Anthropic Reasoning: 25 July 2014 06:00PM
- Sydney Meetup - July: 23 July 2014 07:00PM
- Washington DC: Short Talks: 20 July 2014 03:00PM
Locations with regularly scheduled meetups: Austin, Berkeley, Berlin, Boston, Brussels, Buffalo, Cambridge UK, Canberra, Columbus, London, Madison WI, Melbourne, Mountain View, New York, Philadelphia, Research Triangle NC, Salt Lake City, Seattle, Sydney, Toronto, Vienna, Washington DC, Waterloo, and West Los Angeles. There's also a 24/7 online study hall for coworking LWers.
Claim: Scenario planning is preferable to quantitative forecasting for understanding and coping with AI progress
As part of my work for MIRI on forecasting, I'm considering the implications of what I've read up for the case of thinking about AI. My purpose isn't to actually come to concrete conclusions about AI progress, but more to provide insight into what approaches are more promising and what approaches are less promising for thinking about AI progress.
I've written a post on general-purpose forecasting and another post on scenario analysis. In a recent post, I considered scenario analyses for technological progress. I've also looked at many domains of forecasting and at forecasting rare events. With the knowledge I've accumulated, I've shifted in the direction of viewing scenario analysis as a more promising tool than timeline-driven quantitative forecasting for understanding AI and its implications.
I'll first summarize what I mean by scenario analysis and quantitative forecasting in the AI context. People who have some prior knowledge of the terms can probably skim through the summary quickly. Those who find the summary insufficiently informative, or want to delve deeper, are urged to read my more detailed posts linked above and the references therein.
Quantitative forecasting and scenario analysis in the AI context
The two approaches I am comparing are:
- Quantitative forecasting: Here, specific predictions or forecasts are made, recorded, and later tested against what actually transpired. The forecasts are made in a form where it's easy to score whether they happened. Probabilistic forecasts are also included. These are scored using one of the standard methods to score probabilistic forecasts (such as logarithmic scoring or quadratic scoring).
- Scenario analysis: A number of scenarios of how the future might unfold are generated in considerable detail. Predetermined elements, common to the scenario, are combined with critical uncertainties, that vary between the scenarios. Early indicators that help determine which scenario will transpire are identified. In many cases, the goal is to choose strategies that are robust to all scenarios. For more, read my post on scenario analysis.
Quantitative forecasts are easier to score for accuracy, and in particular offer greater scope for falsification. This has perhaps attracted rationalists more to quantitative forecasting, as a way of distinguishing themselves from what appears to be the more wishy-washy realm of unfalsifiable scenario analysis. In this post, I argue that, given the considerable uncertainty surrounding progress in artificial intelligence, scenario analysis is a more apt tool.
There are probably some people on LessWrong who have high confidence in quantitative forecasts. I'm happy to make bets (financial or purely honorary) on such subjects. However, if you're claiming high certainty while I am claiming uncertainty, I do want to have odds in my favor (depending on how much confidence you express in your opinion), for reasons similar to those that Bryan Caplan described here.
Below, I describe my reasons for preferring scenario analysis to forecasting.
#1: Considerable uncertainty
Proponents of the view that AI is scheduled to arrive in a few decades typically cite computing advances such as Moore's law. However, there's considerable uncertainty even surrounding short-term computing advances, as I described in my scenario analyses for technological progress. When it comes to the question of progress in AI, we have to combine uncertainties in hardware progress with uncertainties in software progress.
Quantitative forecasting methods, such as trend extrapolation, tend to do reasonably well, and might be better than nothing. But they are not foolproof. In particular, the impending death of Moore's law, despite the trend staying quite robust for about 50 years, should make us cautious about too naive an extrapolation of trends. Arguably, simple trend extrapolation is still the best choice relative to other forecasting methods, at least as a general rule. But acknowledging uncertainty and considering multiple scenarios could prepare us a lot better for reality.
In a post in May 2013 titled When Will AI Be Created?, MIRI director Luke Muehlhauser (who later assigned me the forecasting project) looked at the wide range of beliefs about the time horizon for the arrival of human-level AI. Here's how Luke described the situation:
To explore these difficulties, let’s start with a 2009 bloggingheads.tv conversation between MIRI researcher Eliezer Yudkowsky and MIT computer scientist Scott Aaronson, author of the excellent Quantum Computing Since Democritus. Early in that dialogue, Yudkowsky asked:
It seems pretty obvious to me that at some point in [one to ten decades] we’re going to build an AI smart enough to improve itself, and [it will] “foom” upward in intelligence, and by the time it exhausts available avenues for improvement it will be a “superintelligence” [relative] to us. Do you feel this is obvious?
The idea that we could build computers that are smarter than us… and that those computers could build still smarter computers… until we reach the physical limits of what kind of intelligence is possible… that we could build things that are to us as we are to ants — all of this is compatible with the laws of physics… and I can’t find a reason of principle that it couldn’t eventually come to pass…
The main thing we disagree about is the time scale… a few thousand years [before AI] seems more reasonable to me.
Those two estimates — several decades vs. “a few thousand years” — have wildly different policy implications.
After more discussion of AI forecasts as well as some general findings on forecasting, Luke continues:
Given these considerations, I think the most appropriate stance on the question “When will AI be created?” is something like this:
We can’t be confident AI will come in the next 30 years, and we can’t be confident it’ll take more than 100 years, and anyone who is confident of either claim is pretending to know too much.
How confident is “confident”? Let’s say 70%. That is, I think it is unreasonable to be 70% confident that AI is fewer than 30 years away, and I also think it’s unreasonable to be 70% confident that AI is more than 100 years away.
This statement admits my inability to predict AI, but it also constrains my probability distribution over “years of AI creation” quite a lot.
I think the considerations above justify these constraints on my probability distribution, but I haven’t spelled out my reasoning in great detail. That would require more analysis than I can present here. But I hope I’ve at least summarized the basic considerations on this topic, and those with different probability distributions than mine can now build on my work here to try to justify them.
I believe that in the face of this considerable uncertainty, considering multiple scenarios, and the implications of each scenario, can be quite helpful.
#2: Isn't scenario analysis unfalsifiable, and therefore unscientific? Why not aim for rigorous quantitative forecasting instead, that can be judged against reality?
First off, just because a forecast is quantitative doesn't mean it is actually rigorous. I think it's worthwhile to elicit and record quantitative forecasts. These can have high value for near-term horizons, and can provide a rough idea of the range of opinion for longer timescales.
However, simply phoning up experts to ask them for their timelines, or sending them an Internet survey, is not too useful. Tetlock's work, described in Muehlhauser's post and in my post on historical evaluations of forecasting, shows that unaided expert judgment has little value. Asking people who haven't thought through the issue to come up with numbers can give a fake sense of precision with little accuracy (and little genuine precision, either, if we consider the diverse range of responses from different experts). On the other hand, eliciting detailed scenarios from experts can force them to think more clearly about the issues and the relationships between them. Note that there are dangers to eliciting detailed scenarios: people may fall into their own make-believe world. But I think the trade-off with the uncertainty in quantitative forecasting still points in favor of scenario analysis.
Explicit quantitative forecasts can be helpful when people have an opportunity to learn from wrong forecasts and adjust their methodology accordingly. Therefore, I argue that if we want to go down the quantitative forecasting route, it's important to record forecasts about the near and medium future instead of or in addition to forecasts about the far future. Also, providing experts some historical information and feedback at the time they make their forecasts can help reduce the chances of them simply saying things without reflecting. Depending on the costs of recording forecasts, it may be worthwhile to do so anyway, even if we don't have high hopes that the forecasts will yield value. Broadly, I agree with Luke's suggestions:
- Explicit quantification: “The best way to become a better-calibrated appraiser of long-term futures is to get in the habit of making quantitative probability estimates that can be objectively scored for accuracy over long stretches of time. Explicit quantification enables explicit accuracy feedback, which enables learning.”
- Signposting the future: Thinking through specific scenarios can be useful if those scenarios “come with clear diagnostic signposts that policymakers can use to gauge whether they are moving toward or away from one scenario or another… Falsifiable hypotheses bring high-flying scenario abstractions back to Earth.”13
- Leveraging aggregation: “the average forecast is often more accurate than the vast majority of the individual forecasts that went into computing the average…. [Forecasters] should also get into the habit that some of the better forecasters in [an IARPA forecasting tournament called ACE] have gotten into: comparing their predictions to group averages, weighted-averaging algorithms, prediction markets, and financial markets.” See Ungar et al. (2012) for some aggregation-leveraging results from the ACE tournament.
But I argue that the bulk of the effort should go into scenario generation and scenario analysis. Even here, the problem of absence of feedback is acute: we can design scenarios all we want for what will happen over the next century, but we can't afford to wait a century to know if our scenarios transpired. Therefore, it makes sense to break the scenario analysis exercises into chunks of 10-15 years. For instance, one scenario analysis could consider scenarios for the next 10-15 years. For each of the scenarios, we can have a separate scenario analysis exercise that considers scenarios for the 10-15 years after that. And so on. Note that the number of scenarios increases exponentially with the time horizon, but this is simply a reflection of the underlying complexity and uncertainty. In some cases, scenarios could "merge" at later times, as scenarios with slow early progress and fast later progress yield the same end result that scenario with fast early progress and slow later progress do.
#3: Evidence from other disciplines
Explicit quantitative forecasting is common in many disciplines, but the more we look at longer time horizons, and the more uncertainty we are dealing with, the more common scenario analysis becomes. I considered many examples of scenario analysis in my scenario analysis post. As you'll see from the list there, scenario analysis, and variants of it, have become influential in areas ranging from climate change (as seen in IPCC reports) to energy to macroeconomic and fiscal analysis to land use and transportation analysis. And big consulting companies such as McKinsey & Company use scenario analysis frequently in their reports.
It's of course possible to argue that the use of scenario analyses is a reflection of human failing: people don't want to make single forecasts because they are afraid of being proven wrong, or of contradicting other people's beliefs about the future. Or maybe people are shy of thinking quantitatively. I think there is some truth to such a critique. But until we have human-level AI, we have to rely on the failure-prone humans for input on the question of AI progress. Perhaps scenario analysis is superior to quantitative forecasting because humans are insufficiently rational, but to the extent it's superior, it's superior.
Addendum: What are the already existing scenario analyses for artificial intelligence?
I had a brief discussion with Luke Muehlhauser and some of the names below were suggested by him, but I didn't run the final list by him. All responsibility for errors is mine.
To my knowledge (and to the knowledge of people I've talked to) there are no formal scenario analyses of Artificial General Intelligence structured in a manner similar to the standard examples of scenario analyses. However, if scenario analysis is construed sufficiently loosely as a discussion of various predetermined elements and critical uncertainties and a brief mention of different possible scenarios, then we can list a few scenario analyses:
- Nick Bostrom's book Superintelligence (released in the UK and on Kindle, but not released as a print book in the US at the time of this writing) discusses several scenarios for paths to AGI.
- Eliezer Yudkowsky's report on Intelligence Explosion Microeconomics (93 pages, direct PDF link) can be construed as an analysis of AI scenarios.
- Robin Hanson's forthcoming book on em economics discusses one future scenario that is somewhat related to AI progress.
- The Hanson-Yudkowsky AI Foom debate includes a discussion of many scenarios.
The above are scenario analyses for the eventual properties and behavior of an artificial general intelligence, rather than scenario analyses for the immediate future. The work of Ray Kurzwzeil can be thought of as a scenario analysis that lays out an explicit timeline from now to the arrival of AGI.
[QUESTION]: Looking for insights from machine learning that helped improve state-of-the-art human thinking
This question is a follow-up of sorts to my earlier question on academic social science and machine learning.
Machine learning algorithms are used for a wide range of prediction tasks, including binary (yes/no) prediction and prediction of continuous variables. For binary prediction, common models include logistic regression, support vector machines, neural networks, and decision trees and forests.
Now, I do know that methods such as linear and logistic regression, and other regression-type techniques, are used extensively in science and social science research. Some of this research looks at the coefficients of such a model and then re-interprets them.
I'm interesting in examples where knowledge of the insides of other machine learning techniques (i.e., knowledge of the parameters for which the models perform well) has helped provide insights that are of direct human value, or perhaps even directly improved unaided human ability. In my earlier post, I linked to an example (courtesy Sebastian Kwiatkowski) where the results of naive Bayes and SVM classifiers for hotel reviews could be translated into human-understandable terms (namely, reviews that mentioned physical aspects of the hotel, such as "small bedroom", were more likely to be truthful than reviews that talked about the reasons for the visit or the company that sponsored the visit).
PS: Here's a very quick description of how these supervised learning algorithms work. We first postulate a functional form that describes how the output depends on the input. For instance, the functional form in the case of logistic regression outputs the probability as the logistic function applied to a linear combination of the inputs (features). The functional form has a number of unknown parameters. Specific values of the parameters give specific functions that can be used to make predictions. Our goal is to find the parameter values.
We use a huge amount of labeled training data, plus a cost function (which itself typically arises from a statistical model for the nature of the error distribution) to find the parameter values. In the crudest form, this is purely a multivariable calculus optimization problem: choose parameters so that the total error function between the predicted function values and the observed function values is as small as possible. There are a few complications that need to be addressed to get to working algorithms.
So what makes machine learning problems hard? There are a few choice points:
- Feature selection: Figuring out the inputs (features) to use in predicting the outputs.
- Selection of the functional form model
- Selection of the cost function (error function)
- Selection of the algorithmic approach used to optimize the cost function, addressing the issue of overfitting through appropriate methods such as regularization and early stopping.
Of these steps, (1) is really the only step that is somewhat customized by domain, but even here, when we have enough data, it's more common to just throw in lots of features and see which ones actually help with prediction (in a regression model, the features that have predictive power will have nonzero coefficients in front of them, and removing them will increase the overall error of the model). (2) and (3) are mostly standardized, with our choice really being between a small number of differently flavored models (logistic regression, neural networks, etc.). (4) is the part where much of the machine learning research is concentrated: figuring out newer and better algorithms to find (approximate) solutions to the optimization problems for particular mathematical structures of the data.
This is an exposition of some of the main ideas in the paper Robust Cooperation. My goal is to make the ideas and proofs seem natural and intuitive - instead of some mysterious thing where we invoke Löb's theorem at the right place and the agents magically cooperate. Also I hope it is accessible to people without a math or CS background. Be warned, it is pretty cheesy ok.
In a small quirky town, far away from other cities or towns, the most exciting event is a game called (for historical reasons) The Prisoner's Dilemma. Everyone comes out to watch the big tournament at the end of Summer, and you (Alice) are especially excited because this year it will be your first time playing in the tournament! So you've been thinking of ways to make sure that you can do well.
The way the game works is this: Each player can choose to cooperate or defect with the other player. If you both cooperate, then you get two points each. If one of you defects, then that player will get three points, and the other player won't get any points. But if you both defect, then you each get only one point. You have to make your decisions separately, without communicating with each other - however, everyone is required to register the algorithm they will be using before the tournament, and you can look at the other player's algorithm if you want to. You also are allowed to use some outside help in your algorithm.
Now if you were a newcomer, you might think that no matter what the other player does, you can always do better by defecting. So the best strategy must be to always defect! Of course, you know better, if everyone tried that strategy, then they would end up defecting against each other, which is a shame since they would both be better off if they had just cooperated.
But how can you do better? You have to be able to describe your algorithm in order to play. You have a few ideas, and you'll be playing some practice rounds with your friend Bob soon, so you can try them out before the actual tournament.
Your first plan:
I'll cooperate with Bob if I can tell from his algorithm that he'll cooperate with me. Otherwise I'll defect.
For your first try, you'll just run Bob's algorithm and see if he cooperates. But there's a problem - if Bob tries the same strategy, he'll have to run your algorithm, which will run his algorithm again, and so on into an infinite loop!
So you'll have to be a bit more clever than that... luckily you know a guy, Shady, who is good at these kinds of problems.
You call up Shady, and while you are waiting for him to come over, you remember some advice your dad Löb gave you.
(Löb's theorem) "If someone says you can trust them on X, well then they'll just tell you X."
If (someone tells you If [I tell you] X, then X is true)
Then (someone tells you X is true)
(See The Cartoon Guide to Löb's Theorem[pdf] for a nice proof of this)
Here's an example:
Sketchy watch salesman: Hey, if I tell you these watches are genuine then they are genuine!
You: Ok... so are these watches genuine?
Sketchy watch salesman: Of course!
It's a good thing to remember when you might have to trust someone. If someone you already trust tells you you can trust them on something, then you know that something must be true.
On the other hand, if someone says you can always trust them, well that's pretty suspicious... If they say you can trust them on everything, that means that they will never tell you a lie - which is logically equivalent to them saying that if they were to tell you a lie, then that lie must be true. So by Löb's theorem, they will lie to you. (Gödel's second incompleteness theorem)
Despite his name, you actually trust Shady quite a bit. He's never told you or anyone else anything that didn't end up being true. And he's careful not to make any suspiciously strong claims about his honesty.
So your new plan is to ask Shady if Bob will cooperate with you. If so, then you will cooperate. Otherwise, defect. (FairBot)
It's game time! You look at Bob's algorithm, and it turns out he picked the exact same algorithm! He's going to ask Shady if you will cooperate with him. Well, the first step is to ask Shady, "will Bob cooperate with me?"
Shady looks at Bob's algorithm and sees that if Shady says you cooperate, then Bob cooperates. He looks at your algorithm and sees that if Shady says Bob cooperates, then you cooperate. Combining these, he sees that if he says you both cooperate, then both of you will cooperate. So he tells you that you will both cooperate (your dad was right!)
Let A stand for "Alice cooperates with Bob" and B stand for "Bob cooperates with Alice".
From looking at the algorithms, and .
So combining these, .
Then by Löb's theorem, .
Since that means that Bob will cooperate, you decide to actually cooperate.
Bob goes through an analagous thought process, and also decides to cooperate. So you cooperate with each other on the prisoner's dilemma! Yay!
That night, you go home and remark, "it's really lucky we both ended up using Shady to help us, otherwise that wouldn't have worked..."
Your dad interjects, "Actually, it doesn't matter - as long as they were both smart enough to count, it would work. This doesn't just say 'I tell you X', it's stronger than that - it actually says 'Anyone who knows basic arithmetic will tell you X'. So as long as they both know a little arithmetic, it will still work - even if one of them is pro-axiom-of-choice, and the other is pro-axiom-of-life. The cooperation is robust." That's really cool!
But there's another issue you think of. Sometimes, just to be tricky, the tournament organizers will set up a game where you have to play against a rock. Yes, literally just a rock that holding the cooperate button down. If you played against a rock with your current algorithm, well you start by asking Shady if the rock will cooperate with you. Shady is like, "well yeah, duh." So then you cooperate too. But you could have gotten three points by defecting! You're missing out on a totally free point!
You think that it would be a good idea to make sure the other player isn't a complete idiot before you cooperate with them. How can you check? Well, let's see if they would cooperate with a rock placed on the defect button (affectionately known as 'DefectRock'). If they know better than that, and they will cooperate with you, then you will cooperate with them.
The next morning, you excitedly tell Shady about your new plan. "It will be like before, except this time, I also ask you if the other player will cooperate with DefectRock! If they are dumb enough to do that, then I'll just defect. That way, I can still cooperate with other people who use algorithms like this one, or the one from before, but I can also defect and get that extra point when there's just a rock on cooperate."
Shady get's an awkward look on his face, "Sorry, but I can't do that... or at least it wouldn't work out the way you're thinking. Let's say you're playing against Bob, who is still using the old algorithm. You want to know if Bob will cooperate with DefectRock, so I have to check and see if I'll tell Bob that DefectRock will cooperate with him. I would have say I would never tell Bob that DefectRock will cooperate with him. But by Löb's theorem, that means I would tell you this obvious lie! So that isn't gonna work."
Notation, if X cooperates with Y in the prisoner's dilemma (or = D if not).
You ask Shady, does ?
Bob's algorithm: only if .
So to say , we would need .
This is equivalent to , since is an obvious lie.
By Löb's theorem, , which is a lie.
<Extra credit: does the fact that Shady is the one explaining this mean you can't trust him?>
<Extra extra credit: find and fix the minor technical error in the above argument.>
Shady sees the dismayed look on your face and adds, "...but, I know a guy who can vouch for me, and I think maybe that could make your new algorithm work."
So Shady calls his friend T over, and you work out the new details. You ask Shady if Bob will cooperate with you, and you ask T if Bob will cooperate with DefectRock. So T looks at Bob's algorithm, which asks Shady if DefectRock will cooperate with him. Shady, of course, says no. So T sees that Bob will defect against DefectRock, and lets you know. Like before, Shady tells you Bob will cooperate with you, and thus you decide to cooperate! And like before, Bob decides to cooperate with you, so you both cooperate! Awesome! (PrudentBot)
If Bob is using your new algorithm, you can see that the same argument goes through mostly unchanged, and that you will still cooperate! And against a rock on cooperate, T will tell you that it will cooperate with DefectRock, so you can defect and get that extra point! This is really great!!
(ok now it's time for the really cheesy ending)
It's finally time for the tournament. You have a really good feeling about your algorithm, and you do really well! Your dad is in the audience cheering for you, with a really proud look on his face. You tell your friend Bob about your new algorithm so that he can also get that extra point sometimes, and you end up tying for first place with him!
A few weeks later, Bob asks you out, and you two start dating. Being able to cooperate with each other robustly is a good start to a healthy relationship, and you live happily ever after!
In decision theory, we often talk about programs that know their own source code. I'm very confused about how that theory applies to people, or even to computer programs that don't happen to know their own source code. I've managed to distill my confusion into three short questions:
1) Am I uncertain about my own source code?
2) If yes, what kind of uncertainty is that? Logical, indexical, or something else?
3) What is the mathematically correct way for me to handle such uncertainty?
Don't try to answer them all at once! I'll be glad to see even a 10% answer to one question.
I recently stumbled upon an article from early 2003 in Physics World outlining a bit of evidence that some of the constants in nature may change over time. In this particular case, researchers studying quasars noticed that the fine-structure constant (α) might have fluctuated a bit billions of years ago, in both directions (bigger and smaller) with significance 4.1 sigma. What intrigues me about this is that I’ve previously pondered if something like this might be found, albeit for very different reasons.
Back in the 90s I read a book that made a case for the universe as a computer simulation. That particular book wasn’t all that compelling to me, but I’ve never been completely satisfied with arguments against that model and tend to think of the universe generally in those terms anyway. Can I still call myself an atheist if I allow the possibility of a creator in this context? A non-practicing atheist maybe?
If this universe is a computer-generated simulation, programmed by another life form, perhaps the search for extraterrestrial intelligence (SETI) should be expanded to include life forms beyond our universe. It sounds nonsensical, but is it?
If I was to design and code an environment sophisticated enough to allow a species of life to evolve in that environment, I am not convinced that I would have many tools at my disposal to truly be able to understand and evaluate that species very well. Sure, I may be able to see them generating patterns that indicate intelligent life within my simulation, but this life form evolved and exists in an environment completely alien to me. I might have only limited methods at my disposal through which to communicate with them. They would exist in a place that to me is not exactly real and vice-versa.
I’ve always imagined it would be more like evaluating patterns and data readouts or viewing cells through a microscope more than say something like, The Sims. Having designed and implemented the very laws of their universe though, the fundamental constants of the universe could act as a sort of communication channel – one that allows me to at the very least let them know I existed (assuming they were intelligent and were looking). I could modify those constants in such a way over time in much the same manner that we might try to communicate with the more local and familiar concept of alien.
I realize this is all just rambling, but because the alpha is so closely related to those parts of nature that allow for our own existence, it made me take notice, and wonder if this could be some sort of alpha mail. The thought of being able to communicate with an external intelligence is thought provoking enough for me that I decided to write this as my first post here. Who knows? If it ever was confirmed, perhaps we could turn out to be the paper clip maximizer, and we should start looking for our ticket out of here.
This is a thread for rationality-related or LW-related jokes and humor. Please post jokes (new or old) in the comments.
Q: Why are Chromebooks good Bayesians?
A: Because they frequently update!
A super-intelligent AI walks out of a box...
Q: Why did the psychopathic utilitarian push a fat man in front of a trolley?
A: Just for fun.
The official story: "Fifty Shades of Grey" was a Twilight fan-fiction that had over two million downloads online. The publishing giant Vintage Press saw that number and realized there was a huge, previously-unrealized demand for stories like this. They filed off the Twilight serial numbers, put it in print, marketed it like hell, and now it's sold 60 million copies.
The reality is quite different.
I'd like to gauge interest in an (english-language) Tokyo area meetup - given Tokyo's size, if a couple people are interested, it would be good to pick a location/day that's convenient for everybody. Otherwise I will announce a date and time and wait in a cafe with a book hoping that somebody will turn up.
I have been to several LW gatherings and have met consistently awesome and nice people, so if any Tokyo lurkers are reading this, I can assure you it's totally worth it to come! Please make yourself heard in the comments if you are interested.
I don't know very much model theory, and thus I don't fully understand Hutter et al.'s logical prior, detailed here, but nonetheless I can tell you that it uses a very top-down approach. About 60% of what I mean is that the prior is presented as a completed object with few moving parts, which fits the authors' mathematical tastes and proposed abstract properties the function should have. And for another thing, it uses model theory - a dead giveaway.
There are plenty of reasons to take a top-down approach. Yes, Hutter et al.'s function isn't computable, but sometimes the properties you want require uncomputability. And it's easier to come up with something vaguely satisfactory if you don't have to have many moving parts. This can range from "the prior is defined as a thing that fulfills the properties I want" on the lawful good side of the spectrum, to "clearly the right answer is just the exponential of the negative complexity of the statement, duh".
Probably the best reason to use a top-down approach to logical uncertainty is so you can do math to it. When you have some elegant description of global properties, it's a lot easier to prove that your logical probability function has nice properties, or to use it in abstract proofs. Hence why model theory is a dead giveaway.
There's one other advantage to designing a logical prior from the top down, which is that you can insert useful stuff like a complexity penalty without worrying too much. After all, you're basically making it up as you go anyhow, you don't have to worry about where it comes from like you would if you were going form the bottom up.
A bottom-up approach, by contrast, starts with an imagined agent with some state of information and asks what the right probabilities to assign are. Rather than pursuing mathematical elegance, you'll see a lot of comparisons to what humans do when reasoning through similar problems, and demands for computability from the outset.
For me, a big opportunity of the bottom-up approach is to use desiderata that look like principles of reasoning. This leads to more moving parts, but also outlaws some global properties that don't have very compelling reasons behind them.
Before we get to the similarities, rather than the differences, we'll have to impose the condition of limited computational resources. A common playing field, as it were. It would probably serve just as well to extend bottom-up approaches to uncomputable heights, but I am the author here, and I happen to be biased towards the limited-resources case.
The part of top-down assignment using limited resources will be played by a skeletonized pastiche of Paul Christiano's recent report:
i. No matter what, with limited resources we can only assign probabilities to a limited pool of statements. Accordingly, step one is to use some process to choose the set S0 of statements (and their negations) to assign probabilities.
ii. Then we use something a weakened consistency condition (that can be decided between pairs of sentences in polynomial time) to set constraints on the probability function over S0. For example, sentences that are identical except for a double-negation have to be given the same probability.
iii. Christiano constructs a description-length-based "pre-prior" function that is bigger for shorter sentences. There are lots of options for different pre-priors, and I think this is a pretty good one.
iv. Finally, assign a logical probability function over S0 that is as similar as possible to the pre-prior while fulfilling the consistency condition. Christiano measures similarity using cross-entropy between the two functions, so that the problem is one of minimizing cross-entropy subject to a finite list of constraints. (Even if the pre-prior decreases exponentially, this doesn't mean that complicated statements will have exponentially low logical probability, because of the condition from step two that P(a statement) + P(its negation) = 1 - in a state of ignorance, everything still gets probability 1/2. The pre-prior only kicks in when there are more options with different description lengths.)
Next, let's look at the totally different world of a bottom-up assignment of logical probabilities, played here by a mildly rephrased version of my past proposal.
i. Pick a set of sentences S1 to try and figure out the logical probabilities of.
ii. Prove the truth or falsity of a bunch of statements in the closure of S1 under conjugation and negation (i.e. if sentences a and b are in S1, a&b is in the closure of S1).
iii. Assign a logical probability function over the closure of S1 under conjugation with maximum entropy, subject to the constraints proved in part two, plus the constraints that each sentence && its negation has probability 0.
These turn out to be really similar! Look in step three of my bottom-up example - there's a even a sneakily-inserted top-down condition about going through every single statement and checking an aspect of consistency. In the top-down approach, every theorem of a certain sort is proved, while in the bottom-up approach there are allowed to be lots of gaps - but the same sorts of theorems are proved. I've portrayed one as using proofs only about sentences in S0, and the other as using proofs in the entire closure of S1 under conjunction, but those are just points on an available continuum (for more discussion, see Christiano's section on positive semidefinite methods).
The biggest difference is this "pre-prior" thing. On the one hand, it's essential for giving us guarantees about inductive learning. On the other hand, what piece of information do we have that tells us that longer sentences really are less likely? I have unresolved reservations, despite the practical advantages.
A minor confession - my choice of Christiano's report was not coincidental at all. The causal structure went like this:
Last week - Notice dramatic similarities in what gets proved and how it gets used between my bottom-up proposal and Christiano's top-down proposal.
Now - Write post talking about generalities of top-down and bottom-up approaches to logical probability, and then find as a startling conclusion the thing that motivated me to write the post in the first place.
The teeensy bit of selection bias here means that though these similarities are cool, it's hard to draw general conclusions.
So let's look at one more proposal, this one due to Abram Demski, modified by to use limited resources.
i. Pick a set of sentences S2 to care about.
ii. Construct a function on sentences in S2 that is big for short sentences and small for long sentences.
iii. Start with the set of sentences that are axioms - we'll shortly add new sentences to the set.
iv. Draw a sentence from S2 with probability proportional to the function from step two.
v. Do a short consistency check (can use a weakened consistency condition, or just limited time) between this sentence and the sentences already in the set. If it's passed, add the sentence to the set.
vi. Keep doing steps four and five until you've either added or ruled out all the sentences in S2.
vii. The logical probability of a sentence is defined as the probability that it ends up in our set after going through this process. We can find this probability using Monte Carlo by just running the process a bunch of times and counting up what portion of the time each sentences is in the set by the end.
Okay, so this one looks pretty different. But let's look for the similarities. The exact same kinds of things get proved again - weakened or scattershot consistency checks between different sentences. If all you have in S2 are three mutually exclusive and exhaustive sentences, the one that's picked first wins - meaning that the probability function over what sentence gets picked first is acting like our pre-prior.
So even though the method is completely different, what's really going on is that sentences are being given measure that looks like the pre-prior, subject to the constraints of weakened consistency (via rejection sampling) and normalization (keep repeating until all statements are checked).
In conclusion: not everything is like everything else, but some things are like some other things.
Summary: I don't think 'politics is the mind-killer' works well rthetorically. I suggest 'politics is hard mode' instead.
My usual first objection is that it seems odd to single politics out as a “mind-killer” when there’s plenty of evidence that tribalism happens everywhere. Recently, there has been a whole kerfuffle within the field of psychology about replication of studies. Of course, some key studies have failed to replicate, leading to accusations of “bullying” and “witch-hunts” and what have you. Some of the people involved have since walked their language back, but it was still a rather concerning demonstration of mind-killing in action. People took “sides,” people became upset at people based on their “sides” rather than their actual opinions or behavior, and so on.
Unless this article refers specifically to electoral politics and Democrats and Republicans and things (not clear from the wording), “politics” is such a frightfully broad category of human experience that writing it off entirely as a mind-killer that cannot be discussed or else all rationality flies out the window effectively prohibits a large number of important issues from being discussed, by the very people who can, in theory, be counted upon to discuss them better than most. Is it “politics” for me to talk about my experience as a woman in gatherings that are predominantly composed of men? Many would say it is. But I’m sure that these groups of men stand to gain from hearing about my experiences, since some of them are concerned that so few women attend their events.
In this article, Eliezer notes, “Politics is an important domain to which we should individually apply our rationality — but it’s a terrible domain in which to learn rationality, or discuss rationality, unless all the discussants are already rational.” But that means that we all have to individually, privately apply rationality to politics without consulting anyone who can help us do this well. After all, there is no such thing as a discussant who is “rational”; there is a reason the website is called “Less Wrong” rather than “Not At All Wrong” or “Always 100% Right.” Assuming that we are all trying to be more rational, there is nobody better to discuss politics with than each other.
The rest of my objection to this meme has little to do with this article, which I think raises lots of great points, and more to do with the response that I’ve seen to it — an eye-rolling, condescending dismissal of politics itself and of anyone who cares about it. Of course, I’m totally fine if a given person isn’t interested in politics and doesn’t want to discuss it, but then they should say, “I’m not interested in this and would rather not discuss it,” or “I don’t think I can be rational in this discussion so I’d rather avoid it,” rather than sneeringly reminding me “You know, politics is the mind-killer,” as though I am an errant child. I’m well-aware of the dangers of politics to good thinking. I am also aware of the benefits of good thinking to politics. So I’ve decided to accept the risk and to try to apply good thinking there. [...]
I’m sure there are also people who disagree with the article itself, but I don’t think I know those people personally. And to add a political dimension (heh), it’s relevant that most non-LW people (like me) initially encounter “politics is the mind-killer” being thrown out in comment threads, not through reading the original article. My opinion of the concept improved a lot once I read the article.
In the same thread, Andrew Mahone added, “Using it in that sneering way, Miri, seems just like a faux-rationalist version of ‘Oh, I don’t bother with politics.’ It’s just another way of looking down on any concerns larger than oneself as somehow dirty, only now, you know, rationalist dirty.” To which Miri replied: “Yeah, and what’s weird is that that really doesn’t seem to be Eliezer’s intent, judging by the eponymous article.”
Eliezer replied briefly, to clarify that he wasn't generally thinking of problems that can be directly addressed in local groups (but happen to be politically charged) as "politics":
Hanson’s “Tug the Rope Sideways” principle, combined with the fact that large communities are hard to personally influence, explains a lot in practice about what I find suspicious about someone who claims that conventional national politics are the top priority to discuss. Obviously local community matters are exempt from that critique! I think if I’d substituted ‘national politics as seen on TV’ in a lot of the cases where I said ‘politics’ it would have more precisely conveyed what I was trying to say.
But that doesn't resolve the issue. Even if local politics is more instrumentally tractable, the worry about polarization and factionalization can still apply, and may still make it a poor epistemic training ground.
A subtler problem with banning “political” discussions on a blog or at a meet-up is that it’s hard to do fairly, because our snap judgments about what counts as “political” may themselves be affected by partisan divides. In many cases the status quo is thought of as apolitical, even though objections to the status quo are ‘political.’ (Shades of Pretending to be Wise.)
Because politics gets personal fast, it’s hard to talk about it successfully. But if you’re trying to build a community, build friendships, or build a movement, you can’t outlaw everything ‘personal.’
And selectively outlawing personal stuff gets even messier. Last year, daenerys shared anonymized stories from women, including several that discussed past experiences where the writer had been attacked or made to feel unsafe. If those discussions are made off-limits because they relate to gender and are therefore ‘political,’ some folks may take away the message that they aren’t allowed to talk about, e.g., some harmful or alienating norm they see at meet-ups. I haven’t seen enough discussions of this failure mode to feel super confident people know how to avoid it.
Since this is one of the LessWrong memes that’s most likely to pop up in cross-subcultural dialogues (along with the even more ripe-for-misinterpretation “policy debates should not appear one-sided“…), as a first (very small) step, my action proposal is to obsolete the ‘mind-killer’ framing. A better phrase for getting the same work done would be ‘politics is hard mode’:
1. ‘Politics is hard mode’ emphasizes that ‘mind-killing’ (= epistemic difficulty) is quantitative, not qualitative. Some things might instead fall under Middlingly Hard Mode, or under Nightmare Mode…
2. ‘Hard’ invites the question ‘hard for whom?’, more so than ‘mind-killer’ does. We’re used to the fact that some people and some contexts change what’s ‘hard’, so it’s a little less likely we’ll universally generalize.
3. ‘Mindkill’ connotes contamination, sickness, failure, weakness. In contrast, ‘Hard Mode’ doesn’t imply that a thing is low-status or unworthy. As a result, it’s less likely to create the impression (or reality) that LessWrongers or Effective Altruists dismiss out-of-hand the idea of hypothetical-political-intervention-that-isn’t-a-terrible-idea. Maybe some people do want to argue for the thesis that politics is always useless or icky, but if so it should be done in those terms, explicitly — not snuck in as a connotation.
4. ‘Hard Mode’ can’t readily be perceived as a personal attack. If you accuse someone of being ‘mindkilled’, with no context provided, that smacks of insult — you appear to be calling them stupid, irrational, deluded, or the like. If you tell someone they’re playing on ‘Hard Mode,’ that’s very nearly a compliment, which makes your advice that they change behaviors a lot likelier to go over well.
5. ‘Hard Mode’ doesn’t risk bringing to mind (e.g., gendered) stereotypes about communities of political activists being dumb, irrational, or overemotional.
6. ‘Hard Mode’ encourages a growth mindset. Maybe some topics are too hard to ever be discussed. Even so, ranking topics by difficulty encourages an approach where you try to do better, rather than merely withdrawing. It may be wise to eschew politics, but we should not fear it. (Fear is the mind-killer.)
7. Edit: One of the larger engines of conflict is that people are so much worse at noticing their own faults and biases than noticing others'. People will be relatively quick to dismiss others as 'mindkilled,' while frequently flinching away from or just-not-thinking 'maybe I'm a bit mindkilled about this.' Framing the problem as a challenge rather than as a failing might make it easier to be reflective and even-handed.
This is not an attempt to get more people to talk about politics. I think this is a better framing whether or not you trust others (or yourself) to have productive political conversations.
When I playtested this post, Ciphergoth raised the worry that 'hard mode' isn't scary-sounding enough. As dire warnings go, it's light-hearted—exciting, even. To which I say: good. Counter-intuitive fears should usually be argued into people (e.g., via Eliezer's politics sequence), not connotation-ninja'd or chanted at them. The cognitive content is more clearly conveyed by 'hard mode,' and if some group (people who love politics) stands to gain the most from internalizing this message, the message shouldn't cast that very group (people who love politics) in an obviously unflattering light. LW seems fairly memetically stable, so the main issue is what would make this meme infect friends and acquaintances who haven't read the sequences. (Or Dune.)
If you just want a scary personal mantra to remind yourself of the risks, I propose 'politics is SPIDERS'. Though 'politics is the mind-killer' is fine there too.
If you and your co-conversationalists haven’t yet built up a lot of trust and rapport, or if tempers are already flaring, conveying the message ‘I’m too rational to discuss politics’ or ‘You’re too irrational to discuss politics’ can make things worse. In that context, ‘politics is the mind-killer’ is the mind-killer. At least, it’s a needlessly mind-killing way of warning people about epistemic hazards.
‘Hard Mode’ lets you speak as the Humble Aspirant rather than the Aloof Superior. Strive to convey: ‘I’m worried I’m too low-level to participate in this discussion; could you have it somewhere else?’ Or: ‘Could we talk about something closer to Easy Mode, so we can level up together?’ More generally: If you’re worried that what you talk about will impact group epistemology, you should be even more worried about how you talk about it.
In my opinion, living anywhere other than the center of your industry is a mistake. A lot of people — those who don’t live in that place — don’t want to hear it. But it’s true. Geographic locality is still — even in the age of the Internet — critically important if you want to maximize your access to the best companies, the best people, and the best opportunities. You can always cite exceptions, but that’s what they are: exceptions.
- Marc Andreessen
Like many people in the technology industry, I have been thinking seriously about moving to the Bay Area. However, before I decide to move, I want to do a lot of information gathering. Some basic pieces of information - employment prospects, cost of living statistics, and weather averages - can be found online. But I feel that one's quality of life is determined by a large number of very subtle factors - things like walkability, public transportation, housing quality/dollar of rent, lifestyle options, and so on. These kinds of things seem to require first-hand, in-person examination. For that reason, I'm planning to visit the Bay Area and do an in-depth exploration next month, August 20th-24th.
My guess is that a significant number of LWers are also thinking about moving to the Bay Area, and so I wanted to invite people to accompany me in this exploration. Here are some activities we might do:
- Travel around using public transportation. Which places are convenient to get from/to, and which places aren't?
- Visit the offices of the major tech companies like Google, Facebook, Apple, and Twitter. Ask some of their employees how they feel about being a software engineer in Silicon Valley.
- Eat at local restaurants - not so much the fancy/expensive ones, but the ones a person might go to for a typical, everyday lunch outing.
- See some of the sights. Again, the emphasis would be on the things that would affect our everyday lifestyle, should be decide to move, not so much on the tourist attractions. For example, the Golden Gate Bridge is an awesome structure, but I doubt it would improve my everyday life very much. In contrast, living near a good running trail would be a big boost to my lifestyle.
- Do some apartment viewing, to get a feel for how much rent a good/medium/student apartment costs in different areas and how good the amenities are.
- Go to some local LW meetups, if there are any scheduled for the time window.
- Visit the Stanford and UC Berkeley campuses and the surrounding areas.
- Interact with locals and ask them about their experience living in the region
- Visit a number of different neighborhoods, to try to get a sense of the pros and cons of each
- Discuss how to apply Bayesian decision theory to the problem of finding the optimal place to live ;)
If it's worth saying, but not worth its own post (even in Discussion), then it goes here.
Notes for future OT posters:
1. Please add the 'open_thread' tag.
2. Check if there is an active Open Thread before posting a new one.
3. Open Threads should be posted in Discussion, and not Main.
4. Open Threads should start on Monday, and end on Sunday.
The following simple game has one solution that seems correct, but isn’t. Can you figure out why?
Player One moves first. He must pick A, B, or C. If Player One picks A the game ends and Player Two does nothing. If Player One picks B or C, Player Two will be told that Player One picked B or C, but will not be told which of these two strategies Player One picked, Player Two must then pick X or Y, and then the game ends. The following shows the Players’ payoffs for each possible outcome. Player One’s payoff is listed first.
A 3,0 [And Player Two never got to move.]
There has been some talk of a lack of content being posted to Less Wrong, so I decided to start a series on various experiments that I've tried and what I've learned from them as I believe that experimentation is key to being a rationalist. My first few posts will be adapted from content I've written for /r/socialskills, but as Less Wrong has a broader scope I plan to post some original content too. I hope that this post will encourage other people to share detailed descriptions of the experiments that they have tried as I believe that this is much more valuable than a list of lessons posted outside of the context in which they were learned. If anyone has already posted any similar posts, then I would really appreciate any links.
I used to have a lot of trouble in conversation thinking of things to say. I wanted to be a more interesting person and I noticed that my brother uses his knowledge of a broad range of topics to engage people in conversations, so I wanted to do the same.
I was drawn quite quickly towards facts because of how quickly they can be read. If a piece of trivia takes 10 seconds to read, then you can read 360 in an hour. If only 5% are good, then that's still 18 usable facts per hour. Articles are longer, but have significantly higher chances of teaching you something. It seemed like you should be able to prevent ever running out of things to talk about with a reasonable investment of time. It didn't quite work out this way, but this was the idea.d
Another motivation was that I have always valued intelligence and learning more information made me feel good about myself.
Today I learned: #1 recommended source
The straight dope: Many articles in the archive are quite interesting, but I unsubscribed because I found the more recent ones boring
Cracked: Not the most reliable source and can be a huge time sink, but occasionally there are articles there that will give you 6 or 7 interesting facts in one go
Dr Karl: Science blog
I read through the top 1000 links on Today I learned, the entire archive of the straight dope, maybe half of damn interesting and now I know, half of Karl and all the mythbusters results up to about a year or two ago. We are pretty much talking about months of solid reading.
You probably guessed it, but my return on investment wasn't actually that great. I tended to consume this trivia in ridiculously huge batches because by reading all this information I at least felt like I was doing something. If someone came up to me and asked me for a random piece of trivia - I actually don't have that much that I can pull out. It's actually much easier if someone asks about a specific topic, but there's still not that much I can access.
To test my knowledge I decided to pick the first three topics that came into my head and see how much random trivia I could remember about each. As you can see, the results were rather disappointing:
- Cats can survive falls from a higher number of floors better than a lower number of falls because they have a low terminal velocity and more time to orient themselves to ensure they land on their feet
- House cats can run faster than Ursain bolt
- If you are attacked by a dog the best strategy is to shove your hand down its mouth and attack the neck with your other hand
- Dogs can be trained to drive cars (slowly)
- There is such a thing as the world's ugliest dog competition
- Cheese is poisonous to rats
- The existence of rat kings - rats who got their tails stuck together
Knowing these facts does occasionally help me by giving me something interesting to say when I wouldn't have otherwise had it, but quite often I want to quote one of these facts, but I can't quite remember the details. It's hard to quantify how much this helps me though. There have been a few times when I've been able to get someone interested in a conversation that they wouldn't have otherwise been interested in, but I can also go a dozen conversations without quoting any of these facts. No-one has ever gone "Wow, you know so many facts!". Another motivation I had was that being knowledgeable makes me feel good about myself. I don't believe that there was any significant impact in this regard either - I don't have a strong self-concept of myself as someone who is particularly knowledgeable about random facts. Overall this experiment was quite disappointing given the high time investment.
While the social benefits have been extremely minimal, learning all of these facts has expanded my world view.
- I had no idea how crazy nature was: most surprising fact I've learned is that Bluebottles are multiple organisms
- Some of the stuff that the CIA got up to is unbelievable - you'd almost think it came from a conspiracy theorist
- There are many things that you take for granted, but when you think about it, are actually amazing coincidences - moon and sun appearing around the same size
- You don't want to get on the wrong side of the law as it can be horribly unjust
- The government is pretty careless with nuclear weapons. If we can't trust the government can't look after nukes, what can we trust them to look after?
While this technique worked poorly for me, there are many changes that I could have made that might have improved effectiveness.
- Lower batch sizes: when you read too many facts in one go you get tired and it all tends to blur together
- Notes: I started making notes of the most interesting facts I was finding using Evernote. I regularly add new facts, but only very occasionally go back and actually look them up. I was trying to review the new facts that I learned regularly, but I got busy and just fell out of the habit. Perhaps I could have a separate list for the most important facts I learn every week and this would be less effort?
- Rereading saved facts: I did a complete reread through my saved notes once. I still don't think that I have a very good recall - probably related to batch size!
- Spaced repetition: Many people claim that this make memorisation easy
- Thoughtback: This is a lighter alternative to spaced repetition - it gives you notifications on your phone of random facts - about one per day
- Talking to other people: This is a very effective method for remembering facts. That vast majority of facts that I've shared with other people, I still remember. Perhaps I should create a list of facts that I want to remember and then pick one or two at a time to share with people. Once I've shared them a few times, I could move on to the next fact
- Blog posts - perhaps if I collected some of my related facts into blog posts, having to decide which to include and which to not include my help me remember these facts more
- Pausing: I find that I am more likely to remember things if I pause and think that this is something that I want to remember. I was trying to build that habit, but I didn't succeed in this
- Other memory techniques: brains are better at remembering things if you process them. So if you want to remember the story where thieves stole a whole beach in one night, try to picture the beach and then the shock when some surfer turns up and all the sand is gone. Try to imagine what you'd need to pull that off.
I believe that if I had spread my reading out over a greater period of time, then the cost would have been justified. Part of this would have been improved retention and part of this would have been having a new interesting fact to use in conversation every week that I know I hadn't told anyone else before.
The social benefits are rather minimal, so it would be difficult to get them to match up with the time invested. I believe that with enough refinement, someone could improve their effectiveness to the stage where the benefits matched up with the effort invested, but broadening one's knowledge will always be the primary advantage gained.
As most of you may already know, the plane that recently crashed on disputed Ukrainian soil carried some of the world's top HIV researchers.
One part of me holds vehemently that all human beings are of equal value.
Another part of me wishes there could be extra-creative punishments for depriving the world of its best minds.
I asked this question on Facebook here, and got some interesting answers, but I thought it would be interesting to ask LessWrong and get a larger range of opinions. I've modified the list of options somewhat.
What explains why some classification, prediction, and regression methods are common in academic social science, while others are common in machine learning and data science?
For instance, I've encountered probit models in some academic social science, but not in machine learning.
The main algorithms that I believe are common to academic social science and machine learning are the most standard regression algorithms: linear regression and logistic regression.
Possibilities that come to mind:
(0) My observation is wrong and/or the whole question is misguided.
(1) The focus in machine learning is on algorithms that can perform well on large data sets. Thus, for instance, probit models may be academically useful but don't scale up as well as logistic regression.
(2) Academic social scientists take time to catch up with new machine learning approaches. Of the methods mentioned above, random forests and support vector machines was introduced as recently as 1995. Neural networks are older but their practical implementation is about as recent. Moreover, the practical implementations of these algorithm in the standard statistical softwares and packages that academics rely on is even more recent. (This relates to point (4)).
(3) Academic social scientists are focused on publishing papers, where the goal is generally to determine whether a hypothesis is true. Therefore, they rely on approaches that have clear rules for hypothesis testing and for establishing statistical significance (see also this post of mine). Many of the new machine learning approaches don't have clearly defined statistical approaches for significance testing. Also, the strength of machine learning approaches is more exploratory than testing already formulated hypotheses (this relates to point (5)).
(4) Some of the new methods are complicated to code, and academic social scientists don't know enough mathematics, computer science, or statistics to cope with the methods (this may change if they're taught more about these methods in graduate school, but the relative newness of the methods is a factor here, relating to (2)).
(5) It's hard to interpret the results of fancy machine learning tools in a manner that yields social scientific insight. The results of a linear or logistic regression can be interpreted somewhat intuitively: the parameters (coefficients) associated with individual features describe the extent to which those features affect the output variable. Modulo issues of feature scaling, larger coefficients mean those features play a bigger role in determining the output. Pairwise and listwise R^2 values provide additional insight on how much signal and noise there is in individual features. But if you're looking at a neural network, it's quite hard to infer human-understandable rules from that. (The opposite direction is not too hard: it is possible to convert human-understandable rules to a decision tree and then to use a neural network to approximate that, and add appropriate fuzziness. But the neural networks we obtain as a result of machine learning optimization may be quite different from those that we can interpret as humans). To my knowledge, there haven't been attempts to reinterpret neural network results in human-understandable terms, though Sebastian Kwiatkowski's comment on my Facebook post points to an example where the results of naive Bayes and SVM classifiers for hotel reviews could be translated into human-understandable terms (namely, reviews that mentioned physical aspects of the hotel, such as "small bedroom", were more likely to be truthful than reviews that talked about the reasons for the visit or the company that sponsored the visit). But Kwiatkowski's comment also pointed to other instances where the machine's algorithms weren't human-interpretable.
What's your personal view on my main question, and on any related issues?
In early 2000, I registered my personal domain name weidai.com, along with a couple others, because I was worried that the small (sole-proprietor) ISP I was using would go out of business one day and break all the links on the web to the articles and software that I had published on my "home page" under its domain. Several years ago I started getting offers, asking me to sell the domain, and now they're coming in almost every day. A couple of days ago I saw the first six figure offer ($100,000).
In early 2009, someone named Satoshi Nakamoto emailed me personally with an announcement that he had published version 0.1 of Bitcoin. I didn't pay much attention at the time (I was more interested in Less Wrong than Cypherpunks at that point), but then in early 2011 I saw a LW article about Bitcoin, which prompted me to start mining it. I wrote at the time, "thanks to the discussion you started, I bought a Radeon 5870 and started mining myself, since it looks likely that I can at least break even on the cost of the card." That approximately $200 investment (plus maybe another $100 in electricity) is also worth around six figures today.
Clearly, technological advances can sometimes create gold rush-like situations (i.e., first-come-first-serve opportunities to make truly extraordinary returns with minimal effort or qualifications). And it's possible to stumble into them without even trying. Which makes me think, maybe we should be trying? I mean, if only I had been looking for possible gold rushes, I could have registered a hundred domain names optimized for potential future value, rather than the few that I happened to personally need. Or I could have started mining Bitcoins a couple of years earlier and be a thousand times richer.
I wish I was already an experienced gold rush spotter, so I could explain how best to do it, but as indicated above, I participated in the ones that I did more or less by luck. Perhaps the first step is just to keep one's eyes open, and to keep in mind that tech-related gold rushes do happen from time to time and they are not impossibly difficult to find. What other ideas do people have? Are there other past examples of tech gold rushes besides the two that I mentioned? What might be some promising fields to look for them in the future?
Granted, writing is not very effective. But some of us just love writing...
Earning to Give Writing: Which are the places that pay 1USD or more dollars per word?
Clarification Writing: What needs being written because it is only through writing that these ideas will emerge in the first place?
What should we be writing about if we have already been, for very long, training the craft? What has not yet been written, what is the new thing?
I recently realized that, encouraged by LessWrong, I had been using a heuristic in my philosophical reasoning that I now think is suspect. I'm not accusing anybody else of falling into the same trap; I'm just recounting my own situation for the benefit of all.
I actually am not 100% sure that the heuristic is wrong. I hope that this discussion about it generalizes into a conversation about intuition and the relationship between FAI epistemology and our own epistemology.
The heuristic is this: If the ideal FAI would think a certain way, then I should think that way as well. At least in epistemic matters, I should strive to be like an ideal FAI.
Examples of the heuristic in use are:
--The ideal FAI wouldn't care about its personal identity over time; it would have no problem copying itself and deleting the original as the need arose. So I should (a) not care about personal identity over time, even if it exists, and (b) stop believing that it exists.
--The ideal FAI wouldn't care about its personal identity at a given time either; if it was proven that 99% of all observers with its total information set were in fact Boltzmann Brains, then it would continue to act as if it were not a Boltzmann Brain, since that's what maximizes utility. So I should (a) act as if I'm not a BB even if I am one, and (b) stop thinking it is even a meaningful possibility.
--The ideal FAI would think that the specific architecture it is implemented on (brains, computers, nanomachines, giant look-up tables) is irrelevant except for practical reasons like resource efficiency. So, following its example, I should stop worrying about whether e.g. a simulated brain would be conscious.
--The ideal FAI would think that it was NOT a "unified subject of experience" or an "irreducible substance" or that it was experiencing "ineffable, irreducible quale," because believing in those things would only distract it from understanding and improving its inner workings. Therefore, I should think that I, too, am nothing but a physical mechanism and/or an algorithm implemented somewhere but capable of being implemented elsewhere.
--The ideal FAI would use UDT/TDT/etc. Therefore I should too.
--The ideal FAI would ignore uncomputable possibilities. Therefore I should too.
Arguably, most if not all of the conclusions I drew in the above are actually correct. However, I think that the heuristic is questionable, for the following reasons:
(1) Sometimes what we think of as the ideal FAI isn't actually ideal. Case in point: The final bullet above about uncomputable possibilities. We intuitively think that uncomputable possibilites ought to be countenanced, so rather than overriding our intuition when presented with an attractive theory of the ideal FAI (in this case AIXI) perhaps we should keep looking for an ideal that better matches our intuitions.
(2) The FAI is a tool for serving our wishes; if we start to think of ourselves as being fundamentally the same sort of thing as the FAI, our values may end up drifting badly. For simplicity, let's suppose the FAI is designed to maximize happy human life-years. The problem is, we don't know how to define a human. Do simulated brains count? What about patterns found inside rocks? What about souls, if they exist? Suppose we have the intuition that humans are indivisible entities that persist across time. If we reason using the heuristic I am talking about, we would decide that, since the FAI doesn't think it is an indivisible entity that persists across time, we shouldn't think we are either. So we would then proceed to tell the FAI "Humans are naught but a certain kind of functional structure," and (if our overruled intuition was correct) all get killed.
Note 1: "Intuitions" can (I suspect) be thought of as another word for "Priors."
Note 2: We humans are NOT solomonoff-induction-approximators, as far as I can tell. This bodes ill for FAI, I think.
- Australia - Online Hangout: 13 July 2014 06:30PM
- Frankfurt: Goal Factoring: 20 July 2014 02:00PM
- Houston, TX: 12 July 2014 02:00PM
- [Portland] Calibration Training and Potluck - Portland: 12 July 2014 06:31PM
- Upper Canada LW Megameetup: Ottawa, Toronto, Montreal, Waterloo, London: 18 July 2014 07:00PM
The remaining meetups take place in cities with regular scheduling, but involve a change in time or location, special meeting content, or simply a helpful reminder about the meetup:
- Brussels - July meetup: 12 July 2014 01:00PM
- Brussels - August (topic TBD): 09 August 2014 01:00PM
- Canberra: Paranoid Debating: 12 July 2014 06:00PM
- London social meetup - possibly in a park: 13 July 2014 02:00PM
- Sydney Meetup - July: 23 July 2014 07:00PM
- Washington, D.C.: Prisoner's Dilemna tournament: 13 July 2014 03:00PM
Locations with regularly scheduled meetups: Austin, Berkeley, Berlin, Boston, Brussels, Buffalo, Cambridge UK, Canberra, Columbus, London, Madison WI, Melbourne, Mountain View, New York, Philadelphia, Research Triangle NC, Salt Lake City, Seattle, Sydney, Toronto, Vienna, Washington DC, Waterloo, and West Los Angeles. There's also a 24/7 online study hall for coworking LWers.
WARNING: Memetic hazard.
Is there anything we should do?
View more: Next