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IlyaShpitser comments on LINK: AI Researcher Yann LeCun on AI function - Less Wrong
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Comments (82)
Sorry, I am not following you. Decision problems have the form of "What do you do in situation X to maximize a defined utility function?"
It is very easy to transform any causal modeling example into a decision problem. In this case: "here is an observational study where doctors give drugs to some cohort of patients. This is your data. Here's the correct causal graph for this data. Here is a set of new patients from the same cohort. Your utility function rewards you for minimizing patient deaths. Your actions are 'give the drug to everyone in the set' or 'do not give the drug to everyone in the set.' What do you do?"
Predictor algorithms, as understood by the machine learning community, cannot solve this class of problems correctly. These are not abstract problems! They happen all the time, and we need to solve them now, so you can't just say "let's defer solving this until we have a crazy detailed method of simulating every little detail of the way the HIV virus does its thing in these poor people, and the way this drug disrupts this, and the way side effects of the drug happen, etc. etc. etc."
Bayesian network learning and Bayesian network inference can, in principle, solve that problem.
Of course, if your model is wrong, and/or your dataset is degenerate, any approach will give you bad results: Gargbage in, garbage out.
Bayesian networks are statistical, not causal models.
I don't know what you mean by "causal model", but Bayesian networks can deal with the type of problems you describe.
A causal model to me is a set of joint distributions defined over potential outcome random variables.
And no, regardless of how often you repeat it, Bayesian networks cannot solve causal problems.
I have no idea what you're talking about.
gjm asked you what a causal problem was, you didn't provide a definition and instead gave an example of a problem which seems clearly solvable by Bayesian methods such as hidden Markov models (for prediction) or partially observable Markov decision processes (for decision).
(a) Hidden Markov models and POMDPs are probabilistic models, not necessarily Bayesian.
(b) I am using the standard definition of a causal model, first due to Neyman, popularized by Rubin. Everyone except some folks in the UK use this definition now. I am sorry if you are unfamiliar with it.
(c) Statistical models cannot solve causal problems. The number of times you repeat the opposite, while adding the word "clearly" will not affect this fact.
According to Wikipedia:
.
I suppose you mean this.
It seems to be a framework for the estimation of probability distributions from experimental data, under some independence assumptions.
You still didn't define "causal problem" and what you mean by "solve" in this context.
A "Bayesian network" is not necessarily a Bayesian model. Bayesian networks can be used with frequentist methods, and frequently are (see: the PC algorithm). I believe Pearl called the networks "Bayesian" to honor Bayes, and because of the way Bayes theorem is used when you shuffle probabilities around. The model does not necessitate Bayesian methods at all.
I don't mean to be rude, but are we operating at the level of string pattern matching, and google searches here?
Sociological definition : "a causal problem" is a problem that people who do causal inference study. Estimating causal effects. Learning cause-effect relationships from data. Mediation analysis. Interference analysis. Decision theory problems. To "solve" means to get the right answer and thereby avoid going to jail for malpractice.
This is a bizarre conversation. Causal problems aren't something esoteric. Imagine if you kept insisting I define what an algebra problem is. There are all sorts of things you could read on this standard topic.
Looks a like a perfectly normal conversation where people insist on using different terminology sets :-/
You can use frequentists methods to learn Bayesian networks from data, as with any other Bayesian model.
And you can also use Bayesian networks without priors to do things like maximum likelihood estimation, which isn't Bayesian sensu stricto, but I don't think this is relevant to this conversation, is it?
No, we are operating at the level of trying to make sense of your claims.
Please try to reformulate without using the word "cause/causal".
The term has multiple meanings. You may be using a one of them assuming that everybody shares it, but that's not obvious.
Huh?
Can you expand on this, with special attention to the difference between the model and the result of a model, and to the differences from plain-vanilla Bayesian models which will also produce joint distributions over outcomes.
Sure. Here's the world's simplest causal graph: A -> B.
Rubin et al, who do not like graphs, will instead talk about a joint distribution:
p(A, B(a=1), B(a=0))
where B(a=1) means 'random variable B under intervention do(a=1)'. Assume binary A for simplicity here.
A causal model over A,B is a set of densities { p(A, B(a=1), B(a=0) | [ some property ] } The causal model for this graph would be:
{ p(A, B(a=1), B(a=0) | B(a=1) is independent of A, and B(a=0) is independent of A }
These assumptions are called 'ignorability assumptions' in the literature, and they correspond to the absence of confounding between A and B. Note that it took counterfactuals to define what 'absence of confounding' means.
A regular Bayesian network model for this graph is just the set of densities over A and B (since this graph has no d-separation statements). That is, it is the set { p(A,B) | [no assumptions] }. This is a 'statistical model,' because it is a set of regular old joint densities, with no mention of counterfactuals or interventions anywhere.
The same graph can correspond to very different things, you have to specify.
You could also have assumptions corresponding to "missing graph edges." For example, in the instrumental variable graph:
Z -> A -> B, with A <- U -> B, where we do not see U, we would have an assumption that states that B(a,z) = B(a,z') for all a,z,z'.
Please don't say "Bayesian model" when you mean "Bayesian network." People really should say "belief networks" or "statistical DAG models" to avoid confusion.
I do not mean "Bayesian networks". I mean Bayesian models of the kind e.g. described in Gelman's Bayesian Data Analysis.
You still can express this as plain-vanilla conditional densities, can't you? "under intervention do(a=1)" is just a different way of saying "conditional on A=1", no?
and
I don't see counterfactuals in your set of densities and how "interventions" are different from conditionality?
No. If conditioning was the same as interventions I could make it rain by watering my lawn and become a world class athlete by putting on a gold medal.
I don't understand -- can you unroll?
Yes, but what you are describing is a modelling problem. "Is the drug killing them or helping them?" is not a decision problem, although "Which drug should we give them to save their lives?" is. These are two very different problems, possibly with different answers!
Yes, but in the process it becomes a new problem. Although, you are right that modelling is in some respects an 'easier' problem than making decisions. That's also the reason I wrote my top-level comment, saying that it is true that something you can identify in an AI is the ability to model the world.
I guess my point was that there is a trivial reduction (in the complexity theory sense of the word) here, namely that decision theory is "modeling-complete." In other words, if we had algorithm for solving a certain class of decision problems correctly, we automatically have an algorithm for correctly handling the corresponding model (otherwise how could we get the decision problem right?)
Prediction cannot solve causal decision problems, but the reason it cannot is that it cannot solve the underlying modeling problem correctly. (If it could, there is nothing more to do, just integrate over the utility).