Do Bayesian statistics rule the brain?

http://www.mindhacks.com/blog/2008/05/do_bayesian_statisti.html

by dood • 18 years ago

13 26 18 years ago

kurtosis3• 18 years ago

Here's a contrary view: There is a very famous tradition in biology of deriving the form and function of organisms by a mathematical optimization (see D'arcy Thompson). It shouldn't be surprising that the nervous system would converge on Bayesian stats. The dutch book argument shows that any other method of updating beliefs about the world will lose money in a gambling strategy. If "gambling" is replaced by "foraging" or "mating" then Bayes is the optimal way to play. (whether we're playing for the interests of the organism or its genes)

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.

ralphb• 18 years ago

"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.

LPTS7• 18 years ago

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?

kurtosis3• 18 years ago

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.

robg3• 18 years ago

No, but it's as good a description as any for neuronal interactions. The problem though is not with a finite set of connections, but rather the infinite number of possibilities.

eru• 18 years ago

Or rather - very large number of possibilities.

michael_dorfman• 18 years ago

Anyone have a clue as to why (or, indeed, whether) Bayesian mathematics work any better than the more old-school neural network algorithms?

socksandsandals• 18 years ago

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.

robg3• 18 years ago

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.

kurtosis3• 18 years ago

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.

schtog3• 18 years ago

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.

gnaritas3• 18 years ago

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.

LPTS7• 18 years ago

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.

andreyf• 18 years ago

No, or we wouldn't suck at Bayesian statistics so much:

http://en.wikipedia.org/wiki/Base_rate_fallacy

Do Bayesian statistics rule the brain?

Related Stories