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Qiaochu_Yuan comments on Evidential Decision Theory, Selection Bias, and Reference Classes - Less Wrong
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???
How are you supposed to make good decisions?
Well, I am trying to learn why people think EDT isn't terminally busted. I gave a simple example that usually breaks EDT as I understand it, and I hope someone will work out the right answer with EDT to show me where I am going wrong.
Use decision theory. The point is that it's not decision theory that tells you your shoelaces are undone when you look at your feet. "Are my shoelaces undone?" is a purely epistemic question, that has nothing to do with making decisions. But upon finding out that your shoelaces are undone, a decision theory might decide to do X or Y, after discovering (by making a few queries to the epistemic-calculations module of your brain) that certain actions will result in the shoelaces being tied again, that that would be safer, etc etc.
You're complaining that EDT is somehow unable to solve the question of "is HAART bad" given some useless data set when that doesn't even sound like a question EDT should be trying to answer in the first place—but rather, a question you would try to answer with standard multivariate statistics.
Ok -- a patient comes in (from the same reference class as the patients in your data). This patient has HIV. Do you put him on HAART or not? Your utility function is minimizing patient deaths. By the way, if you do the wrong thing, you go to jail for malpractice.
How about we dispense with this and you tell us if you know how to extract information about the usefulness (or not) of HAART from a data set like this?
Ok, first things first.
Do you agree that "Do you put him on HAART or not? Your utility function is minimizing patient deaths." is in fact a kind of question EDT, or decision theories in general, should be trying to answer?
In fact, I already said elsewhere in this thread that I think there is the right answer to this question, and this right answer is to put the patient on HAART (whereas my understanding of EDT is that it will notice that E[death | HAART] > E[death | no HAART], and conclude that HAART is bad). The way you get the answer is no secret either, it's what is called 'the g-formula' or 'truncated factorization' in the literature. I have been trying to understand how my understanding of EDT is wrong. If people's attempt to fix this is to require that we observe all unobserved confounders for death, then to me this says EDT is not a very good decision theory (because other decision theories can get the right answer here without having to observe anything over what I specified). If people say that the right answer is to not give HAART then that's even worse (e.g. they will kill people and go to jail if they actually practice medicine like that).
Yes. However a decision theory in general contains no specific prescriptions for obtaining probabilities from data, such as "oh, use the parametric g-formula". In general, they have lists of probabilistic information that they require.
Setting that aside, I assume you mean the above to mean "count the proportion of samples without HAART with death, and compare to proportion of samples with HAART with death". Ignoring the fact that I thought there were no samples without HAART at t=0, what if half of the samples referred to hamsters, rather than humans?
No-one would ever have proposed EDT as a serious decision theory if they intended one to blindly count records while ignoring all other relevant "confounding" information (such as species, or health status). In reality, the purpose of the program of "count the number of people who smoke who have the lesion" or "count how many people who have HAART die" is to obtain estimates of P(I have the lesion | I smoke) or P(this patient dies | I give this patient HAART). That is why we discard hamster samples, because there are good a priori reasons to think that the survival of hamsters and humans is not highly correlated, and "this patient" is a human.
Well, there is in reality A0 and A1. I choose this example because in this example it is both the case that E[death | A0, A1] is wrong, and \sum_{L0} E[death | A0,A1,L0] p(L0) (usual covariate adjustment) is wrong, because L0 is a rather unusual type of confounder. This example was something naive causal inference used to get wrong for a long time.
More generally, you seem to be fighting the hypothetical. I gave a specific problem on only four variables, where everything is fully specified, there aren't hamsters, and which (I claim) breaks EDT. You aren't bringing up hamsters with Newcomb's problem, why bring them up here? This is just a standard longitudinal design: there is nothing exotic about it, no omnipotent Omegas or source-code reading AIs.
I think you misunderstand decision theory. If you were right, there would be no difference between CDT and EDT. In fact, the entire point of decision theories is to give rules you would use to make decisions. EDT has a rule involving conditional probabilities of observed data (because EDT treats all observed data as evidence). CDT has a rule involving a causal connection between your action and the outcome. This rule implies, contrary to what you claimed, that a particular method must be used to get your answer from data (this method being given by the theory of identification of causal effects) on pain of getting garbage answers and going to jail.
I said why I was bringing them up. To make the point that blindly counting the number of events in a dataset satisfying (action = X, outcome = Y) is blatantly ridiculous, and this applies whether or not hamsters are involved. If you think EDT does that then either you are mistaken, or everyone studying EDT are a lot less sane than they look.
The difference is that CDT asks for
P(utility | do(action), observations)and EDT asks forP(utility | action, observations). Neither CDT or EDT specify detailed rules for how to calculate these probabilities or update on observations, or what priors to use. Indeed, those rules are normally found in statistics textbooks, Pearl's Causality or—in the case of the g-formula—random math papers.Ok. I keep asking you, because I want to see where I am going wrong. WIthout fighting the hypothetical, what is EDT's answer in my hamster-free, perfectly standard longitudinal example: do you in fact give the patient HAART or not? If you think there are multiple EDTs, pick the one that gives the right answer! My point is, if you do give HAART, you have to explain what rule you use to arrive at this, and how it's EDT and not CDT. If you do not give HAART, you are "wrong."
The form of argument where you say "well, this couldn't possibly be right -- if it were I would be terrified!" isn't very convincing. I think Homer Simpson used that once :).
What I meant was "if it were, that would require a large number of (I would expect) fairly intelligent mathematicians to have made an egregiously dumb mistake, on the order of an engineer modelling a 747 as made of cheese". Does that seem likely to you? The principle of charity says "don't assume someone is stupid so you can call them wrong".
Regardless, since there is nothing weird going on here, I would expect (a particular non-strawman version of) EDT's answer to be precisely the same as CDT's answer, because "agent's action" has no common causes with the relevant outcomes (ETA: no common causes that aren't screened off by observations. If you measure patient vital signs and decide based on them, obviously that's a common cause, but irrelevant since you've observed them). In which case you use whatever statistical techniques one normally uses to calculate
P(utility | do(action), observations)(the g-formula seems to be an ad-hoc frequentist device as far as I can tell, but there's probably a prior that leads to the same result in a bayesian calculation). You keep telling me that results in "give HAART" so I guess that's the answer, even though I don't actually have any data.Is that a satisfying answer?
In retrospect, I would have said that before, but got distracted by the seeming ill-posedness of the problem and incompleteness of the data. (Yes, the data is incomplete. Analysing it requires nontrivial assumptions, as far as I can tell from reading a paper on the g-formula.)