A common task facing computational scientists and, arguably, the brains of primates more generally is to construct models for data, particularly ones that invoke latent variables. Although it is often natural to identify the latent variables of such a model with the true unobserved variables in the world, the correspondence between the two can be more complicated, as when the former are instantiated by the firing rates of neurons in the cortex, and the latter are (e.g.) locations of objects in 2D space. Nevertheless, a simple desideratum for the model’s latent variables can be formulated in any case: that inference to them from the observations throw away no information about the true latent variables. It may then be surprising to learn that two models that explain the data equally well–indeed, as well as possible–can differ under this criterion.

In statistics, the task of learning a model for data can be formalized as density estimation. We propose and prove sufficient conditions for latent-variable density estimation that guarantees satisfaction of the criterion just proposed–“information retention,” for short; show the connection of this criterion to results on multisensory integration in neuroscience and psychology; and use it to derive a recurrent version of a density estimator, the restricted Boltzmann machine, that we call the “recurrent exponential-family harmonium.”

This work was done in collaboration with M.R. Fellows, B.K. Dichter, and P.N. Sabes (supervisor) at UCSF.