Richard Zemel, Peter Dayan
Most theoretical and empirical studies of population codes make the assumption that underlying neuronal activities is a unique and unambiguous value of an encoded quantity. However, population activities can contain additional information about such things as multiple values of or uncertainty about the quantity. We have pre(cid:173) viously suggested a method to recover extra information by treat(cid:173) ing the activities of the population of cells as coding for a com(cid:173) plete distribution over the coded quantity rather than just a single value. We now show how this approach bears on psychophys(cid:173) ical and neurophysiological studies of population codes for mo(cid:173) tion direction in tasks involving transparent motion stimuli. We show that, unlike standard approaches, it is able to recover mul(cid:173) tiple motions from population responses, and also that its output is consistent with both correct and erroneous human performance on psychophysical tasks.
A population code can be defined as a set of units whose activities collectively encode some underlying variable (or variables). The standard view is that popu(cid:173) lation codes are useful for accurately encoding the underlying variable when the individual units are noisy. Current statistical approaches to interpreting popula(cid:173) tion activity reflect this view, in that they determine the optimal single value that explains the observed activity pattern given a particular model of the noise (and possibly a loss function). In our work, we have pursued an alternative hypothesis, that the population en(cid:173) codes additional information about the underlying variable, including multiple values and uncertainty. The Distributional Population Coding (DPC) framework finds the best probability distribution across values that fits the population activity (Zemel, Dayan, & Pouget, 1998). The DPC framework is appealing since it makes clear how extra information can be conveyed in a population code. In this paper, we use it to address a particu-
Distributional Population Codes and Multiple Motion Models