Combining Probabilistic Population Codes

Abstract

We study the problem of statistically correct inference in networks whose basic representations are population codes. Population codes are ubiquitous in the brain, and involve thesimultaneous activity ofmany units coding for some low dimensional quantity. A classic example are place cells in the rat hippocampus: these re when the animal is at a particular place in an environment, so the underlying quantity has two dimensions of spatial location. We show howtointerpret the activity as encoding whole probability distributions over the underlying variable rather then just single values, and propose a method of inductively learning mappings between population codes that are computationally tractable and yet o er good approximations to statistically optimal inference. We simulate the method on some simple examples to prove its competence. In a population code, information about some lowdimensional quantity (such as the position of a visual feature) is represented in the activity of a collection of units, each responding to a limited range of stimuli within this low-dimensional space. Strong evidence exists for this form of coding at the sensory input areas of the brain (eg retinotopic and tonotopic maps) as well as at the motor output level [Georgopoulos et al., 1986]. Evidence is mounting that many other intermediate neural processing areas also use population codes [Tanaka, 1996]. Certain important questions about population codes have been extensively investigated, including how toextract an optimal underlying value [Salinas and Abbott, 1994� Snippe, 1996] and how to learn such representations [Kohonen, 1982]. However, two important issues have been almost ignored (with the important exception of [Anderson, 1994]). One is the treatment of population codes as encoding whole probability density functions (PDFs) over the underlying quantities rather than just a single