Do Bayesian statistics rule the brain?(mindhacks.com)
mindhacks.com
Do Bayesian statistics rule the brain?
http://www.mindhacks.com/blog/2008/05/do_bayesian_statisti.html
26 comments
"But saying that the brain is Bayesian is not that profound."
And, furthermore, it's not really a new idea.
Judea Pearls work in the late 80's suggested something along these lines. I have also seen suggested that some of Marvin Minskys groundlaying work back in the 60's pointed in this direction, but YMMV on that one.
And, furthermore, it's not really a new idea.
Judea Pearls work in the late 80's suggested something along these lines. I have also seen suggested that some of Marvin Minskys groundlaying work back in the 60's pointed in this direction, but YMMV on that one.
You obviously know more about the science and math here than I do. So I'm offering these thoughts deferentially. I'm coming at this as a jack of all trades type who did a ton of philosophy of mind and cognitive science stuff in college but somewhat deficient with the hard science.
"What priors are being modeled"
I think this is the most interesting thing. There is so much information about how memories are recreated as you remember them, and about memory being unreliable. Even if you had an answer to the question "what priors are being modeled?", it would need to be indexed to a time. Indexing your question to times is where it gets interesting.
This would create a question that would be a lot harder and necessary to understand to get at the truth of this. Something like "How can the constantly changing sea of fragmented memories we base our idea of self on serve as reliable priors at all." Or, less poetically and more formally:
Given a person, P, at 2 times, T1 and T2, and two sets of priors, M1 and M2, such that M1 and M2 belong to P, at T1 and T2, respectively, and between T1 and T2, P obtained exactly one datum, D, what is the relationship between M1 at T1 in P, and (M2-D) at T2 in P?
And, generally, what calculus explains the relationship between Mx at Tx in P, and (My-Dn) at Ty in P, where Dn is the sum of the data P acquired between Tx and Ty?
I don't think M1 is equivalent to M2-D in the first, and I don't think that My-Dn is equivalent to Mx in the second. I think all the evidence about memories being inconsistent, recreated, count towards my intuition. I also think the way things like a sudden smell can cause priming of memories, or an emotional state can alter memory recall suggest this.
"how is inference implemented with neurons"
This seems like the most trivial, least profound, and most uninteresting part. We know that the brain does these inferences, and we know that even very simple systems based on cellular automation can be turing complete and make inferences. The particular details will not shed light on the fundamental problems understanding mind.
"what constraints, or "hyperparameters" are built into these priors."
It sounds to me like their idea that hallucinations and delusions as breakdowns of Bayesian statistics functionality would bear fruit that could answer this question, although I don't have an answer.
I also wonder, wasn't "the brain is ruled by electricity" a profound insight for it's time?
"What priors are being modeled"
I think this is the most interesting thing. There is so much information about how memories are recreated as you remember them, and about memory being unreliable. Even if you had an answer to the question "what priors are being modeled?", it would need to be indexed to a time. Indexing your question to times is where it gets interesting.
This would create a question that would be a lot harder and necessary to understand to get at the truth of this. Something like "How can the constantly changing sea of fragmented memories we base our idea of self on serve as reliable priors at all." Or, less poetically and more formally:
Given a person, P, at 2 times, T1 and T2, and two sets of priors, M1 and M2, such that M1 and M2 belong to P, at T1 and T2, respectively, and between T1 and T2, P obtained exactly one datum, D, what is the relationship between M1 at T1 in P, and (M2-D) at T2 in P?
And, generally, what calculus explains the relationship between Mx at Tx in P, and (My-Dn) at Ty in P, where Dn is the sum of the data P acquired between Tx and Ty?
I don't think M1 is equivalent to M2-D in the first, and I don't think that My-Dn is equivalent to Mx in the second. I think all the evidence about memories being inconsistent, recreated, count towards my intuition. I also think the way things like a sudden smell can cause priming of memories, or an emotional state can alter memory recall suggest this.
"how is inference implemented with neurons"
This seems like the most trivial, least profound, and most uninteresting part. We know that the brain does these inferences, and we know that even very simple systems based on cellular automation can be turing complete and make inferences. The particular details will not shed light on the fundamental problems understanding mind.
"what constraints, or "hyperparameters" are built into these priors."
It sounds to me like their idea that hallucinations and delusions as breakdowns of Bayesian statistics functionality would bear fruit that could answer this question, although I don't have an answer.
I also wonder, wasn't "the brain is ruled by electricity" a profound insight for it's time?
I've always thought of Noam Chomsky's "language acquisition device" as a kind of prior on the space of languages that's hardwired into the brain. The process of learning a language consists of fitting the parameters of this model to the sense data that each child is immersed in. Of course Bayes' rule provides one way to update our guess about the parameters of this model given the current data but who knows if that's what's really going on. I think the evidence is pretty strong that this flexibility in the space of priors over language only lasts a for small precious window until we become adults, and then we're all stuck with lame accents. So it does indeed have some time dependence.
When I was talking about the implementation of inference I was referring to the people doing experiments trying to figure out the "neural code" - Questions like: how much information is conveyed by a single spike? Is there any meaning in the rate of the spikes? How much information is there in a coincidence when two or more neurons fire simultaneously? What rules govern the plasticity of the activation or inhibition relationships among neurons? Does any of this have anything to do with probability? A great book on this is "Spikes" by de Ruyter and Bialek et. al.
I didn't mean to sound dismissive about the electricity thing - I think hodgkin and huxley were both given medicine nobels for their work on the nerves. I guess the electricity thing really goes back the 1700's when galvani made a dead frog move with electric current.
When I was talking about the implementation of inference I was referring to the people doing experiments trying to figure out the "neural code" - Questions like: how much information is conveyed by a single spike? Is there any meaning in the rate of the spikes? How much information is there in a coincidence when two or more neurons fire simultaneously? What rules govern the plasticity of the activation or inhibition relationships among neurons? Does any of this have anything to do with probability? A great book on this is "Spikes" by de Ruyter and Bialek et. al.
I didn't mean to sound dismissive about the electricity thing - I think hodgkin and huxley were both given medicine nobels for their work on the nerves. I guess the electricity thing really goes back the 1700's when galvani made a dead frog move with electric current.
"I think the evidence is pretty strong that this flexibility in the space of priors over language only lasts a for small precious window until we become adults, and then we're all stuck with lame accents."
I think this is true for most people, not everyone.
If this is true for most people, we can locate these differences by comparing autistic people who quickly acquire languages as adults with normal people. It's interesting that autistic people skilled with language often don't have noticeable accents in that language, even with a language they learn in adulthood.
This flexibility in the space of languages involves a honing of perception. As you learn your first language, you become better at perceiving the sounds of that language, but your ability to perceive the sounds of another language go down. For example, a person who speaks exclusively english speaker cannot discern between sounds that would have different meanings that a chinese speaker would easily hear.
(Deferentially), I think you are wrong about where the hardwiring occurs. I think the hardwiring that limits most peoples ability to learn language arises is perception, not the space of priors. I believe if you could change the hardwiring that occurs in making sensory discriminations relevant to the language, the "space of priors" would still show the ability to learn language. It's true that there is a precious window for most people to learn languages, but that's because the perceptual paths get hardwired, not the memory and processing that make up what we seem to be calling the "space of priors"
But, that's not the scale of time dependance I was thinking. Even if the scale of time dependence was 5 seconds, and the new data was just seeing it was raining out, the way your brain understands the concept of rain involves accessing memories it destroys and recreates as part of recognizing "rain", as well as the particulars of your emotional state and what's going into your sense of smell, so much that the set of priors 5 seconds before would be different then the ones now, even if you took out the information about it raining.
I think this is true for most people, not everyone.
If this is true for most people, we can locate these differences by comparing autistic people who quickly acquire languages as adults with normal people. It's interesting that autistic people skilled with language often don't have noticeable accents in that language, even with a language they learn in adulthood.
This flexibility in the space of languages involves a honing of perception. As you learn your first language, you become better at perceiving the sounds of that language, but your ability to perceive the sounds of another language go down. For example, a person who speaks exclusively english speaker cannot discern between sounds that would have different meanings that a chinese speaker would easily hear.
(Deferentially), I think you are wrong about where the hardwiring occurs. I think the hardwiring that limits most peoples ability to learn language arises is perception, not the space of priors. I believe if you could change the hardwiring that occurs in making sensory discriminations relevant to the language, the "space of priors" would still show the ability to learn language. It's true that there is a precious window for most people to learn languages, but that's because the perceptual paths get hardwired, not the memory and processing that make up what we seem to be calling the "space of priors"
But, that's not the scale of time dependance I was thinking. Even if the scale of time dependence was 5 seconds, and the new data was just seeing it was raining out, the way your brain understands the concept of rain involves accessing memories it destroys and recreates as part of recognizing "rain", as well as the particulars of your emotional state and what's going into your sense of smell, so much that the set of priors 5 seconds before would be different then the ones now, even if you took out the information about it raining.
if bayesian probability is how the brain works, why is it so hard for most people to understand this:
http://en.wikipedia.org/wiki/Monty_Hall_problem
seriously, even the most clever people even have huge trouble grasping it.
seriously, even the most clever people even have huge trouble grasping it.
Because people don't necessarily have a conscience understanding of how the lower layers of their minds work. Being a Bayesian neural network doesn't imply you understand Bayesian neural networks in general.
Even if your brain is ruled by Bayesian statistics, that doesn't make YOU a bayesian neural network, or even tell us much about identity at all (that would be to confuse the hard and easy problems of consciousness). But your point about a bayesian network not having to understand other bayesian networks stands, and is the right answer to the guy you responded too.
You're correct, however, we still haven't defined what you actually is yet. Conscienceless could merely be an illusion or as Jeff Hawkins says, it could merely be what it feels like to have a neocortex.
I do reject the idea that conscienceless is anything more than the byproduct of the physical process of the brain, of course, I don't think that's what you're implying, I hope.
I do reject the idea that conscienceless is anything more than the byproduct of the physical process of the brain, of course, I don't think that's what you're implying, I hope.
I didn't mean to imply anything about my beliefs. I have a more general atheoretic attitude towards it. My belief could be formalized "For any person with a set of beliefs about consciousness, their beliefs are wrong, and they are not justified in holding them."
You said: "I do reject the idea that conscienceless is anything more than the byproduct of the physical process of the brain, of course, I don't think that's what you're implying, I hope."
This is exactly like saying: "I reject the idea that final digits of pi is anything more than the byproduct of the physical processes in my computer's calculator program"
I don't think actually I implied not-physicalism, but I would be happy to endorse it.
The idea that consciousness is illusory relates to high functioning autism in people who develop the theories in a complicated way. Ludwig Wittgenstein, for example, had a very autistic picture theory of language that gave way to a non-autistic theory as he got older. For very intelligent people who are blind to other minds, studying consciousness is very important, because, to them, it seems like the most logical way to understand people. I don't mean this as criticism of intelligent people with autism. But, relying on these people to understand consciousness is like relying on a colorblind person who has mastered scientific and mathematical models of analyzing wavelengths of light to explain color as an artist experiences it.
You said: "I do reject the idea that conscienceless is anything more than the byproduct of the physical process of the brain, of course, I don't think that's what you're implying, I hope."
This is exactly like saying: "I reject the idea that final digits of pi is anything more than the byproduct of the physical processes in my computer's calculator program"
I don't think actually I implied not-physicalism, but I would be happy to endorse it.
The idea that consciousness is illusory relates to high functioning autism in people who develop the theories in a complicated way. Ludwig Wittgenstein, for example, had a very autistic picture theory of language that gave way to a non-autistic theory as he got older. For very intelligent people who are blind to other minds, studying consciousness is very important, because, to them, it seems like the most logical way to understand people. I don't mean this as criticism of intelligent people with autism. But, relying on these people to understand consciousness is like relying on a colorblind person who has mastered scientific and mathematical models of analyzing wavelengths of light to explain color as an artist experiences it.
This is exactly like saying: "I reject the idea that final digits of pi is anything more than the byproduct of the physical processes in my computer's calculator program"
I reject the idea that pi has any final digits. :-)
I reject the idea that pi has any final digits. :-)
Well, that's exactly the point. I cribbed that line from a poem I wrote:
Trying to find / the explanation of why we are conscious / in patterns in the brain / is like / trying to find / the last digit of pi / in the circuitry of a scientific calculator
Trying to find / the explanation of why we are conscious / in patterns in the brain / is like / trying to find / the last digit of pi / in the circuitry of a scientific calculator
Anyone have a clue as to why (or, indeed, whether) Bayesian mathematics work any better than the more old-school neural network algorithms?
The reasons why the neural network model failed and Bayesian inference is much more applicable are described very well by Jeff Hawkins in his book "On Intelligence" (http://onintelligence.com/). I highly recommend it, if just for the the questions and trains of thoughts it raises.
Honestly, I think it just comes down to simplicity. Bayesian algorithms tend to make fewer assumptions a priori. By contrast, look at something like backprop.
I respectfully disagree:
Bayesian methods do not necessarily make fewer assumptions. They just allow you to make your assumptions explicit and to evaluate how sensitive your conclusions were to those assumptions. Conventional statistical methods all have ways of doing this but they are ad hoc. In this sense you are totally correct - bayes is simpler.
Also because bayesian inference in any interesting problem domain is often computationally impossible, you must make approximations - which adds even more complexity.
Backpropagation on the other hand, is remarkably simple -- it's just the chain rule from calculus.
Bayesian methods do not necessarily make fewer assumptions. They just allow you to make your assumptions explicit and to evaluate how sensitive your conclusions were to those assumptions. Conventional statistical methods all have ways of doing this but they are ad hoc. In this sense you are totally correct - bayes is simpler.
Also because bayesian inference in any interesting problem domain is often computationally impossible, you must make approximations - which adds even more complexity.
Backpropagation on the other hand, is remarkably simple -- it's just the chain rule from calculus.
this was interesting.
is bayesian compuatation for "big interesting" problems NP-complete? learning them is? http://www.google.se/search?client=firefox-a&rls=org.moz... http://citeseer.ist.psu.edu/120871.html
then what does the brain do? approximations as well? or bayesian networks are just a good model of the brain but far from complete? does it suggests in some similar way to the http://en.wikipedia.org/wiki/Uncertainty_principle that there is a limit to what we can know in this aspect(if thats what the uncertainty principle suggests for that part of physics?)?
where is this Eliezer Yudkowsky guy? come and give your opinion please!
is bayesian compuatation for "big interesting" problems NP-complete? learning them is? http://www.google.se/search?client=firefox-a&rls=org.moz... http://citeseer.ist.psu.edu/120871.html
then what does the brain do? approximations as well? or bayesian networks are just a good model of the brain but far from complete? does it suggests in some similar way to the http://en.wikipedia.org/wiki/Uncertainty_principle that there is a limit to what we can know in this aspect(if thats what the uncertainty principle suggests for that part of physics?)?
where is this Eliezer Yudkowsky guy? come and give your opinion please!
I think any similarities between the uncertainty principle in physics and limits of what we can know about our minds is poetic or formal.
There might be some rule which the uncertainty principle, the mind problem, and Godel's incompleteness fall out of, or that relates them eloquently and definitively at a higher order of abstraction, but they aren't the same.
I think there is a common kind of error equivocating the hard problem of consciousness (which is a formal way of understanding your "limit to what we can know in this aspect") with uncertainty principle or Godel's Incompleteness (another idea that looks like and is confused with the uncertainty principle or the hard problem of consciousness if you squint right). It is like recognizing y=2X^2 and y=2X^2+2 have the same derivative, but using this insight to argue that 2X^2=2X^2+2.
There might be some rule which the uncertainty principle, the mind problem, and Godel's incompleteness fall out of, or that relates them eloquently and definitively at a higher order of abstraction, but they aren't the same.
I think there is a common kind of error equivocating the hard problem of consciousness (which is a formal way of understanding your "limit to what we can know in this aspect") with uncertainty principle or Godel's Incompleteness (another idea that looks like and is confused with the uncertainty principle or the hard problem of consciousness if you squint right). It is like recognizing y=2X^2 and y=2X^2+2 have the same derivative, but using this insight to argue that 2X^2=2X^2+2.
good points. more on the subject:
http://en.wikipedia.org/wiki/G%C3%B6del%27s_incompleteness_t...
Minds and machines
Hilary Putnam (1960) suggested that while Gödel's theorems cannot be applied to humans, since they make mistakes and are therefore inconsistent, it may be applied to the human faculty of science or mathematics in general. If we are to believe that it is consistent, then either we cannot prove its consistency, or it cannot be represented by a Turing machine.
http://en.wikipedia.org/wiki/Mechanism_%28philosophy%29#G.C3...
http://en.wikipedia.org/wiki/G%C3%B6del%27s_incompleteness_t...
Minds and machines
Main article: Mechanism (philosophy)#Gödelian arguments
Hilary Putnam (1960) suggested that while Gödel's theorems cannot be applied to humans, since they make mistakes and are therefore inconsistent, it may be applied to the human faculty of science or mathematics in general. If we are to believe that it is consistent, then either we cannot prove its consistency, or it cannot be represented by a Turing machine.
http://en.wikipedia.org/wiki/Mechanism_%28philosophy%29#G.C3...
"In this sense you are totally correct - bayes is simpler."
That's exactly the sense I referring to and similarly the error correction terms (i/o) in backprop.
But I mis-read the original question: Either "works" just fine - it's just that there seems to be a movement away from NN and toward Bayes. That's what I was answering even as it's tough to judge that right now. Still, NN seemed much hotter 10 years ago in the literature. Where's Google Trends for academic papers?
That's exactly the sense I referring to and similarly the error correction terms (i/o) in backprop.
But I mis-read the original question: Either "works" just fine - it's just that there seems to be a movement away from NN and toward Bayes. That's what I was answering even as it's tough to judge that right now. Still, NN seemed much hotter 10 years ago in the literature. Where's Google Trends for academic papers?
If the brain uses bayesian inference, could emotions and intuitions perhaps be functionally equivalent to the approximations needed to do the impossible computations you are talking about?
people who froze up when confronted with incomplete information about probabilities of outcomes were out competed by those who did something, even if they chose wrong a lot of the time.
That's an interesting thought.
No, or we wouldn't suck at Bayesian statistics so much:
http://en.wikipedia.org/wiki/Base_rate_fallacy
http://en.wikipedia.org/wiki/Base_rate_fallacy
But saying that the brain is Bayesian is not that profound. It's like saying that the brain is ruled by electricity. The key is what priors are being modeled, how is inference implemented with neurons, and what constraints, or "hyperparameters" are built into these priors.