Bayesian Fundamentalism or Enlightenment?

Dec 05 2010 Published by under Blogging on Peer-Reviewed Research

"Whatever society at large views as its most powerful device tends to become our means for thinking about the brain, even in formal scientific settings. Despite the recurring tendency to take the current metaphor literally, it is important to recognize that any metaphor will eventually be supplanted. Thus, researchers should be aware of what the current metaphor contributes to their theories, as well as what the theories’ logical content is once the metaphor is stripped away."

Jones & Love, 2011

While surfing the web for preprints, I found an upcoming Brain and Behavioral Sciences (BBS) release by Matt Jones and Brad Love which I would highly recommend as thought-provoking, lucid and approachable reading material.  It's entitled : "Bayesian Fundamentalism or Enlightenment?  On the Explanatory Status and Theoretical Contributions of Bayesian Models of Cognition" and it's part intellectual history, part rigorous scientific critique.  I should preface this by saying that I am not a Bayesian modeler, and while I'm acquainted with Bayes' laws and have read some Bayesian papers on language acquisition -- which mostly led to yawning and quiet grumbling about how they'd set up the problem wrong -- I am not in the best position to assess the merits of the arguments in this paper.  So I won't.  I just really liked reading it.  I'm eagerly anticipating the full BBS article, which, I'm assuming, will include responses from Tenenbaum, Griffiths, Chater and the rest of the Bayes high court.  If their replies are anything like their conference demeanor, it's going to be fun..

If you've read this far, and you're not familiar with Bayes' law, the Internet is chalk full of Bayesian fanatics, so a little Googling should find you a decent tutorial, like this one.  I do suggest reading it too : there have been dozens of articles lately in the popular science press about the application of this kind of probability modeling to, for example, medical statistics.

Now, if you're not familiar with the journal, that's something else entirely -- and must be remedied!  BBS is a excellent resource for getting your head around a problem, because it allows researchers to meticulously advance a new claim, or set of claims, and then invites scholars in their discipline to submit a one-page reply.  For scholars and the lay public alike, this is a brilliant means of both highlighting the issue and clarifying the positions at stake.

To get an idea of how this works, it's worth taking a look at this classic Boroditsky & Ramscar (2001) reply to an early Bayesian BBS article.  B&R somehow manage to make the entire contents of the abstract a joke.  (You'll see what I mean).

Excerpts, after the jump:

First, briefly, here's the abstract for Boroditsky & Ramscar (2001):

There is an old joke about a theoretical physicist who was charged with figuring out how to increase the milk production of cows. Although many farmers, biologists, and psychologists had tried and failed to solve the problem before him, the physicist had no trouble coming up with a solution on the spot. “First,” he began, “we assume a spherical cow . . .

And here's a slightly abridged abstract for Jones & Love (2011):

Bayesian modeling of cognition has undergone a recent rise in prominence, due largely to mathematical advances in specifying and deriving predictions from complex probabilistic models. Much of this research aims to demonstrate that cognitive behavior can be explained from rational principles alone, without recourse to psychological or neurological processes and representations. ...We identify a number of challenges that limit the rational program’s potential contribution to psychological theory. Specifically, rational Bayesian models are significantly unconstrained, both because they are uninformed by a wide range of process-level data and because their assumptions about the environment are generally not grounded in empirical measurement. The psychological implications of most Bayesian models are also unclear. Bayesian inference itself is conceptually trivial, but strong assumptions are often embedded in the hypothesis sets and the approximation algorithms used to derive model predictions, without a clear delineation between psychological commitments and implementational details. Comparing multiple Bayesian models of the same task is rare, as is the realization that many Bayesian models recapitulate existing (mechanistic-level) theories. Despite the expressive power of current Bayesian models, we argue they must be developed in conjunction with mechanistic considerations to offer substantive explanations of cognition.

They then propose to lay out "several means for such an integration" which will allow the Bayesian program to avoid "the pitfalls that have plagued other theoretical movements."  By which they mean behaviorism, connectionism and evolutionary psychology.  I've selected some choice excerpts from the paper, but be sure to read it in full if you've got a bone to pick since I'm quoting outside the full frame of their arguments:

On Bayes qua psychological theory

"Taken as a psychological theory, the Bayesian framework does not have much to say. Its most unambiguous claim is that much of human behavior can be explained by appeal to what is rational or optimal. This is an old idea that has been debated for centuries (e.g., Kant, 1787/1961). More importantly, rational explanations for behavior offer no guidance as to how that behavior is accomplished. ...The Bayesian framework is more radical in that, unlike previous brain metaphors grounded in technology and machines, the Bayesian metaphor is tied to a mathematical ideal and thus eschews mechanism altogether. This makes Bayesian models more difficult to evaluate. By locating explanations firmly at the computational level, the Bayesian Fundamentalist program renders irrelevant many major modes of scientific inquiry, including physiology, neuroimaging, reaction time, heuristics and biases, and much of cognitive development."

On the mathematical complexity of Bayesian models

"The elaborate mathematics that often arises in Bayesian models comes from the complexity of their hypothesis sets or the tricks used to derive tractable predictions, which generally have little to do with the psychological claims of the researchers. Bayesian inference itself, aside from its assumption of optimality and close relation to vote-counting models, is surprisingly devoid of psychological substance. It involves no representations to be updated; no encoding, storage, retrieval, or search; no attention or control; no reasoning or complex decision processes; and in fact no mechanism at all, except for a simple counting rule."

On the fractionated nature of the Bayesian program

"Just as mechanistic modeling allows for alternative assumptions about process and representation, rational modeling allows for alternative assumptions about the environment in which the cognitive system is situated (Anderson, 1990). In both cases, a principal scientific goal is to decide which assumptions provide the best explanation. With Bayesian models, the natural approach dictated by rational analysis is to make the generative model faithful to empirical measurements of the environment. However, ...this empirical grounding is rarely carried out in practice. Consequently, the rational program loses much of its principled nature, and models of different tasks become fractionated because there is nothing but the math of Bayesian inference to bind them together."

On unacknowledged assumptions in Bayesian models

"there are generally multiple rational theories of any given task, corresponding to different assumptions about the environment and the learner’s goals. Consequently, there is insufficient acknowledgement of these assumptions and their critical roles in determining model predictions. It is extremely rare to find a comparison among alternative Bayesian models of the same task to determine which is most consistent with empirical data (see Fitelson, 1999, for a related analysis of the philosophical literature). Likewise, there is little recognition when the critical assumptions of a Bayesian model logically overlap closely with those of other theories, so that the Bayesian model is expressing essentially the same explanation, just couched in a different framework"

"Bayesian models often depend on complex hypothesis spaces based on elaborate and mathematically complex assumptions about environmental dynamics. As the emphasis is generally on rational inference (i.e., starting with the assumptions of the generative model and deriving optimal behavior from there), the assumptions themselves generally receive little scrutiny. The combination of these two factors leads to a dangerously under-constrained research program, in which the core assumptions of a model (i.e., the choice of hypothesis space) can be made at the modeler’s discretion, without comparison to alternatives and without any requirement to fit physiological or other process-level data."

On the problem of assuming optimality, more generally

"In addition to the rejection of mechanistic explanation, a central principle of the Fundamentalist Bayesian approach to cognition is that of optimality. ...Completely sidestepping mechanistic considerations when considering optimality leads to absurd conclusions. To illustrate, it may not be optimal or evolutionarily advantageous to ever age, become infertile, and die, but these outcomes are universal and follow from biological constraints. It would be absurd to seriously propose an optimal biological entity that is not bounded by these biological and physical realities, but this is exactly the reasoning Bayesian Fundamentalists follow when formulating theories of cognition."

On the (mis)application of Bayesian modeling to developmental psychology

"Although rational Bayesian modeling has a large footprint in developmental psychology, development presents basic challenges to the rational approach. One key question for any developmental model is what develops. In rational models, the answer is that nothing develops. Rational models are mechanism free, leaving only information sampled to change over time.  ...[This observation] put rational theories of development in a difficult position."

On the proposal of 'optimization under constraints'

"Although the general research strategy based on bounded rationality can be fruitful, it severely limits the meaning of labeling a behavior as rational or optimal. Characterizing capacity limitations is essentially an exercise in characterizing the mechanism, which represents a departure from rational principles. Once all capacity limitations are detailed, notions of rationality lose force. To provide a perverse example, each person can be viewed as an optimal version of himself given his own limitations, flawed beliefs, motivational limitations, etc. At such a point, it is not clear what work the rational analysis is doing."

On the need to make our assumptions clear

"it may be impossible in cases to specify what is optimal in any general sense without considering the nature of the mechanism. All of these questions can have multiple possible answers, and finding which answers lead to the best explanation of the data is part of the scientific challenge. Just as with mechanistic models, competing alternatives need to be explicitly recognized and compared."

These excerpts follow mainly from their critique of Bayesian Fundamentalism.  If you want to get into the meat of their alternative proposal, read the paper!

5 responses so far

  • Yoder says:

    Um. Looks like you have the wrong address for the Boroditsky & Ramscar (2001) link.

  • marcus says:

    Great post.

    I'm not sold on Bayesianism and don't know if I ever will be. I don't think it is useless. I'm all for multiple accounts in the literature to get people to think about things in different ways. Researchers who use these models have put out some interesting papers and sparked a lot of good discussion.

    However, I cannot imagine that things will continue like that for the next 20 or 30 years. I guess my opinion of Bayesian models is based on my opinion of the the future direction cognitive research. I would think that links between behavior and biology will become more specified and detailed. Of the computational modeling styles used by folks who are interested in behavior, Bayesian modeling seems the least ready for accounting for biology and cognitive theory (some would say it doesn't do either). I know that some Bayesian modelers have made some handwavey gestures about biology but I haven't seen anything to make me think that will happen any time soon. The other styles of modeling certainly have their issues, but they seem to have much more potential for growth. The use of Bayes rule in modeling may prove useful, but purely Bayesian modeling seems like a garden path to me.

  • Whenever the topic of modelling comes up, I always think back to a talk given by Florin Cutzu to the Psych department shortly after he came to IU. He's a computer scientist who studies machine vision, and his talk was about some psychophysical data and a neural network model. Well, actually, the whole talk was about the psychophysical data because he knew that was the empirical work that could have gone one way or another. He finished with the sentence "And the model captures all this, because I made it so it would".

    I've always thought that was the right way to think about most models, especially Bayesian ones. People get so excited by the fact they produce a behaviour, and miss the point that, well, of course they do - if they didn't, it's because you've built it wrong. It's really hard to model in a way where you constrain it so that it might not work - although not impossible., and it's a lot more interesting to do it this way.