The randomized control trial is a great example where a superintelligence actually could do better by using a non-random strategy. Ideally, an AI could take its whole prior into account and do a value of information calculation. Even if it had no useful prior, that would just mean that any method of choosing is equally “random” under the the AI’s knowledge.
Bayesian adaptive clinical trial designs place subjects in treatment groups based on a posterior distribution. (Clinical trials accrue patients gradually, so you don’t have to assign the patients using the prior: you assign new patients using the posterior conditioned on observations of the current patients.)
These adaptive trials are, as you conjecture, much more efficient than traditional randomized trials.
Example: I-SPY 2.
Assigns patients to treatments based on their “biomarkers” (biological measurements made on the patients) and the posterior derived from previous patients.
When I heard one of the authors explain adaptive trials in a talk, he said they were based on multi-armed bandit theory, with a utility function that combines accuracy of results with welfare of the patients in the trial.
However, unlike in conventional multi-armed bandit theory, the trial design still makes random decisions! The trials are still sort of randomized: “adaptively randomized,” with patients having a higher chance of being assigned to certain groups than others, based on the current posterior distribution.
JWW suggests that an AI could partition trial subjects into control and experimental groups such that expected number of events in both was equal, and presumably also such that cases involving assumptions were distributed equally, to minimize the impact of assumptions. For instance, an AI doing a study of responses to an artificial sweetener could do some calculations to estimate the impact of each gene on sugar metabolism, then partition subjects so as to balance their allele frequencies for those genes.
(A more extreme interpretation would be that the AI is partitioning subjects and performing the experiment not in a way designed to test a single hypothesis, but to maximize total information extracted from the experiment. This would be optimal, but a radical departure from how we do science. Actually, now that I think of it, I wrote a grant proposal suggesting this 7 years ago. My idea was that molecular biology must now be done by interposing a layer of abstraction via computational intelligence in between the scientist and the data, so that the scientist is framing hypotheses not about individual genes or proteins, but about causes, effects, or systems. It was not well-received.)
There’s another comment somewhere countering this idea by noting that this almost requires omniscience; the method one uses to balance out one bias may introduce another.
This doesn’t require omniscience, or AI: people do this now (based on info they have). If you have more info, we know how to use it (there is theory). Why are we talking about AI, this is a math problem.
Slightly harshly worded suggestion (not to you specifically): maybe more reading, less invocation of robo-Jesus in vain.
Eliezer claims that randomness is always bad; many other people claim that one way randomness is good is that it is unbiased. Partitioning subjects into experimental conditions must be unbiased. Using an algorithm and knowing that its biases are orthogonal to the phenomenon being investigated requires omniscience. Besides, if you knew in advance what was relevant, you wouldn’t need to do the experiment.
That is what the comment means. The use of the term “AI” is just to show that the claim is that no real-world agent can be smart enough to do unbiased partitioning in all cases, not just that we’re not smart enough to do it.
In practice, a possibly biased but intelligent partitioning is better when the sample size is small.
We know what property we want (that randomization will give you), good balance in relevant covariates between two groups. I can use a deterministic algorithm for this, and in fact people do, e.g. matching algorithms. Another thing people do is try all possible assignments (see: permutation tests for the null).
Discussion of AI and omniscience is a complete red herring, you don’t need that to show that you don’t need randomness for this. We aren’t randomizing for the sake of randomizing, we are doing it because we want some property that we can directly target deterministically.
I don’t think EY can possibly know enough math to make his claim go through, I think this is an “intellectual marketing” claim. People do this a lot, if we are talking about your claim, you won the game.
If you sort all the subjects on one criteria, it may be correlated in an unexpected way with another criteria you’re unaware of. Suppose you want to study whether licorice causes left-handedness in a population from Tonawanda, NY. So you get a list of addresses from Tonawanda New York, sort them by address, and go down the list throwing them alternately into control and experimental group. Then you mail the experimental group free licorice for a ten years. Voila, after 10 years there are more left-handers in the experimental group.
But even and odd addresses are on opposite sides of the street. And it so happens that in Tonawanda, NY, the screen doors on the front of every house are hinged on the west side, regardless of which way the house faces, because the west wind is so strong it would rip the door off its hinges otherwise. So people on the north side of the street, who are mostly in your experimental group, open the door with their left hand, getting a lot of exercise from this (the wind is very strong), while people on the south side open the screen door with their right hand.
It seems unlikely to me that many hidden correlations would survive alternating picks from a sorted list like this rigged example, but if the sample size is large enough, you’d still be better off randomizing than following any deterministic algorithm, because “every other item from a list sorted on X” has low Kolmogorov complexity and can be replicated by an unknown correlate of your observable variable by chance.
Eliezer claims that randomness is always bad; many other people claim that one way randomness is good is that it is unbiased. Partitioning subjects into experimental conditions must be unbiased.
This is perhaps a useful place to illustrate the “randomness hath no power” argument: randomness is unbiased in expectation but we actually expect the absolute amount of biasedness for a randomly selected assignment to be nonzero. When biasing factors are known ahead of time, we do better by controlling for it directly (with, say, a paired assignment).
Exactly! This is a math problem! And it becomes a very complicated math problem very quickly as the prior information gets interesting.
There’s nothing magical about an AI; it can’t figure out anything a human couldn’t figure out in principle. The difference is the “superintelligence” bit: a superintelligent AI could efficiently use much more complicated prior information for experiment design.
I don’t understand the improvement you think is possible here. In a lot of cases, the math isn’t the problem, the theory is known. The difficulty is usually finding a large enough sample size,etc.
There is a lot of statistical literature on optimal experimental design, and it’s used all the time. Years ago at Intel, we spent a lot of time on optimal design of quality control measurements, and I have no doubt a lot of industrial scientists in other companies spend their time thinking about such things.
The problem is, information is a model dependent concept (derivatives of log-likelihood depend on the likelihood), so if your prior isn’t fairly strong, there isn’t a lot of improvement to be had. A lot of science is exploratory, trying to optimize the experimental design is premature.
Either way, this isn’t stuff you need an AI for at all, it’s stuff people talk about and think about now, today, using computer assisted human intellect.
I’m going to commit a social faux pas and respond to my own comment, because multiple subthreads are all saying essentially the same thing: this is just math, the theory is known, humans can already do it (often with some help from computers to get through the math).
As I’ve read it, one of the major takeaways of lesswrong is that AI is not magical. If humans cannot possibly figure out the theory, neither can an AI. If humans cannot possibly do the math (possibly with some help from a computer), neither can an AI. Anything an AI can do, a human can also do in principle. They differ only in the degree: AIs will eventually be able to do much more complicated math, solve much more complicated problems, and self-improve much faster and more reliably.
So if you look at my original suggestion and think “that’s nothing special, a human can do that in theory” then you’re completely correct. Things humans can do IN THEORY are EXACTLY the things with which an AI can help.
The randomized control trial is a great example where a superintelligence actually could do better by using a non-random strategy. Ideally, an AI could take its whole prior into account and do a value of information calculation. Even if it had no useful prior, that would just mean that any method of choosing is equally “random” under the the AI’s knowledge.
AI != perfectly rational agent
Ideally = perfectly rational agent
so why did you mention an ‘AI’?
Bayesian adaptive clinical trial designs place subjects in treatment groups based on a posterior distribution. (Clinical trials accrue patients gradually, so you don’t have to assign the patients using the prior: you assign new patients using the posterior conditioned on observations of the current patients.)
These adaptive trials are, as you conjecture, much more efficient than traditional randomized trials.
Example: I-SPY 2. Assigns patients to treatments based on their “biomarkers” (biological measurements made on the patients) and the posterior derived from previous patients.
When I heard one of the authors explain adaptive trials in a talk, he said they were based on multi-armed bandit theory, with a utility function that combines accuracy of results with welfare of the patients in the trial.
However, unlike in conventional multi-armed bandit theory, the trial design still makes random decisions! The trials are still sort of randomized: “adaptively randomized,” with patients having a higher chance of being assigned to certain groups than others, based on the current posterior distribution.
I don’t understand this comment at all.
JWW suggests that an AI could partition trial subjects into control and experimental groups such that expected number of events in both was equal, and presumably also such that cases involving assumptions were distributed equally, to minimize the impact of assumptions. For instance, an AI doing a study of responses to an artificial sweetener could do some calculations to estimate the impact of each gene on sugar metabolism, then partition subjects so as to balance their allele frequencies for those genes.
(A more extreme interpretation would be that the AI is partitioning subjects and performing the experiment not in a way designed to test a single hypothesis, but to maximize total information extracted from the experiment. This would be optimal, but a radical departure from how we do science. Actually, now that I think of it, I wrote a grant proposal suggesting this 7 years ago. My idea was that molecular biology must now be done by interposing a layer of abstraction via computational intelligence in between the scientist and the data, so that the scientist is framing hypotheses not about individual genes or proteins, but about causes, effects, or systems. It was not well-received.)
There’s another comment somewhere countering this idea by noting that this almost requires omniscience; the method one uses to balance out one bias may introduce another.
This doesn’t require omniscience, or AI: people do this now (based on info they have). If you have more info, we know how to use it (there is theory). Why are we talking about AI, this is a math problem.
Slightly harshly worded suggestion (not to you specifically): maybe more reading, less invocation of robo-Jesus in vain.
Eliezer claims that randomness is always bad; many other people claim that one way randomness is good is that it is unbiased. Partitioning subjects into experimental conditions must be unbiased. Using an algorithm and knowing that its biases are orthogonal to the phenomenon being investigated requires omniscience. Besides, if you knew in advance what was relevant, you wouldn’t need to do the experiment.
That is what the comment means. The use of the term “AI” is just to show that the claim is that no real-world agent can be smart enough to do unbiased partitioning in all cases, not just that we’re not smart enough to do it.
In practice, a possibly biased but intelligent partitioning is better when the sample size is small.
We know what property we want (that randomization will give you), good balance in relevant covariates between two groups. I can use a deterministic algorithm for this, and in fact people do, e.g. matching algorithms. Another thing people do is try all possible assignments (see: permutation tests for the null).
Discussion of AI and omniscience is a complete red herring, you don’t need that to show that you don’t need randomness for this. We aren’t randomizing for the sake of randomizing, we are doing it because we want some property that we can directly target deterministically.
I don’t think EY can possibly know enough math to make his claim go through, I think this is an “intellectual marketing” claim. People do this a lot, if we are talking about your claim, you won the game.
If you sort all the subjects on one criteria, it may be correlated in an unexpected way with another criteria you’re unaware of. Suppose you want to study whether licorice causes left-handedness in a population from Tonawanda, NY. So you get a list of addresses from Tonawanda New York, sort them by address, and go down the list throwing them alternately into control and experimental group. Then you mail the experimental group free licorice for a ten years. Voila, after 10 years there are more left-handers in the experimental group.
But even and odd addresses are on opposite sides of the street. And it so happens that in Tonawanda, NY, the screen doors on the front of every house are hinged on the west side, regardless of which way the house faces, because the west wind is so strong it would rip the door off its hinges otherwise. So people on the north side of the street, who are mostly in your experimental group, open the door with their left hand, getting a lot of exercise from this (the wind is very strong), while people on the south side open the screen door with their right hand.
It seems unlikely to me that many hidden correlations would survive alternating picks from a sorted list like this rigged example, but if the sample size is large enough, you’d still be better off randomizing than following any deterministic algorithm, because “every other item from a list sorted on X” has low Kolmogorov complexity and can be replicated by an unknown correlate of your observable variable by chance.
This is perhaps a useful place to illustrate the “randomness hath no power” argument: randomness is unbiased in expectation but we actually expect the absolute amount of biasedness for a randomly selected assignment to be nonzero. When biasing factors are known ahead of time, we do better by controlling for it directly (with, say, a paired assignment).
Exactly! This is a math problem! And it becomes a very complicated math problem very quickly as the prior information gets interesting.
There’s nothing magical about an AI; it can’t figure out anything a human couldn’t figure out in principle. The difference is the “superintelligence” bit: a superintelligent AI could efficiently use much more complicated prior information for experiment design.
I don’t understand the improvement you think is possible here. In a lot of cases, the math isn’t the problem, the theory is known. The difficulty is usually finding a large enough sample size,etc.
There is a lot of statistical literature on optimal experimental design, and it’s used all the time. Years ago at Intel, we spent a lot of time on optimal design of quality control measurements, and I have no doubt a lot of industrial scientists in other companies spend their time thinking about such things.
The problem is, information is a model dependent concept (derivatives of log-likelihood depend on the likelihood), so if your prior isn’t fairly strong, there isn’t a lot of improvement to be had. A lot of science is exploratory, trying to optimize the experimental design is premature.
Either way, this isn’t stuff you need an AI for at all, it’s stuff people talk about and think about now, today, using computer assisted human intellect.
Designing experiments to get more information than just evidence for a single hypothesis is old hat.
I’m going to commit a social faux pas and respond to my own comment, because multiple subthreads are all saying essentially the same thing: this is just math, the theory is known, humans can already do it (often with some help from computers to get through the math).
As I’ve read it, one of the major takeaways of lesswrong is that AI is not magical. If humans cannot possibly figure out the theory, neither can an AI. If humans cannot possibly do the math (possibly with some help from a computer), neither can an AI. Anything an AI can do, a human can also do in principle. They differ only in the degree: AIs will eventually be able to do much more complicated math, solve much more complicated problems, and self-improve much faster and more reliably.
So if you look at my original suggestion and think “that’s nothing special, a human can do that in theory” then you’re completely correct. Things humans can do IN THEORY are EXACTLY the things with which an AI can help.