Monday, November 4, 2013

Some thoughts on Marcus & Davis (2013)

(...and a little also on Jones & Love 2011)

One of the things that struck me about Marcus & Davis (2013) [M&D] is that they seem to be concerned with identifying what the priors are for learning. But what I'm not sure of is how you distinguish the following options:

(a) sub-optimal inference over optimal priors
(b) optimal inference over sub-optimal priors
(c) sub-optimal inference over sub-optimal priors

M&D seem to favor option (a), but I'm not sure there's an obvious reason to do so. Jones & Love 2011 [J&L] mention the possibility of "bounded rationality", which is something like "be as optimal as possible in your inference, given the prior and the processing limitations you have". That sounds an awful lot like (c), and seems like a pretty reasonable option to explore. The concern in general with what the priors are actually dovetails quite nicely with traditional linguistic explorations of how to define (constrain) the learner's hypothesis space appropriately to make successful inference possible. Also, J&L are quite aware of this too, and underscore the importance of selecting the priors appropriately.

That being said, no matter what priors and inference processes end up working, there's clear utility in being explicit about all the assumptions that yield a match to human behavior, which M&D want (and I'm a huge fan of this myself: see my commentary on a recent article here where I happily endorse this). Once you've identified the necessary pieces that make a learning strategy work, you can then investigate (or at least discuss) which assumptions are necessarily optimal.  That may not be an easy task, but it seems like a step in the right direction.

M&D seem to be unhappy with probabilistic models as a default assumption - and okay, that's fine. But it does seem important to recognize that probabilistic reasoning is a legitimate option. And maybe some of cognition is probabilistic and some isn't - I don't think there's a compelling reason to believe that cognition has to be all one or all the other. (I mean, after all, cognition is made up of a lot of different things.) In this vein, I think a reasonable thing that M&D would like is for us to not just toss out non-probabilistic options that work really well solely because they're non-probabilistic.

On a related note, I very much agree with one of the last things M&D note, which is that we should be explicit about "what would constitute evidence that a probabilistic approach is not appropriate for a particular task or domain".  I'm not sure myself what that evidence would look like, since even categorical behavior can be simulated by a probabilistic model that just thresholds. Maybe if it's more "economical" (however we define that) to not have a probabilistic model, and there exists a non-probabilistic model that accomplishes the same thing?

A few comments about Jones & Love 2011 [J&L]:

J&L seem very concerned with the recent focus in the Bayesian modeling world on existence proofs for various aspects of cognition.  They do mention later in their article (around section 6, I think), that existence proofs are a useful starting point, however -- they just don't want research to stop there. An existence proof that a Bayesian learning strategy can work for some problem should be the first step for getting a particular theory on the table as a real possibility worth considering (e.g., whatever's in the priors for that particular learning strategy that allowed Bayesian inference to succeed, as well as the Bayesian inference process itself).

Overall, J&L seem to make a pretty strong call for process models (i.e., algorithmic-level models, instead of just computational-level models). Again, this seems like a natural follow-up once you have a computational-level model you're happy with.  So the main point is simply not to rest on your Bayesian inference laurels once you have your existence proof at the computational level for some problem in cognition.  The Chater et al. 2011 commentary to J&L note that many Bayesian modelers are moving in this direction already, creating "rational process" models.


Chater, N., Goodman, N., Griffiths, T., Kemp, C., Oaksford, M., & Tenenbaum, J. 2011. The imaginary fundamentalists: The unshocking truth about Bayesian cognitive science. Behavioral and Brain Sciences, 34 (4), 194-196.

Jones, M. & Love, M. 2011. Bayesian Fundamentalism or Enlightenment? On the explanatory status and theoretical contributions of Bayesian models of cognition. Behavioral and Brain Sciences, 34 (4), 169-188.

Pearl, L. 2013. Evaluating strategy components: Being fair.  [lingbuzz]

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