Bayes' optimal inference, decision making, and learning with Probabilistic Population Codes
Jeff Beck
University of Rochester

Human behavior has been shown to take uncertainty into account when combining ambiguous cues and to do so in a Bayes' optimal way. This particular computation requires a neural code which represents entire probability distribution functions rather than simply estimates. Moreover, this code must be structured so that the operations available to neural circuits are, in fact, capable of implementing (and learn to implement) optimal cue combination and action selection. Here, we will show how the Probabilistic Population Coding (PPC) framework naturally links biological constraints on neural operations with an optimal form of variability that leads to specific predictions regarding stimulus conditioned neural statistics. As an example, we will show how the requirement that optimal cue combination be performed by linear operations implies that neural variability should exhibit tuning curve like behavior with arbitrary correlations and fixed (but not necessarily unit) Fano factors. We will then show that this particular form of neural variability is makes it possible to optimally implement other useful probabilistic operations such as posterior diffusion/saliency, maximum likelihood estimation, and information maximization via the neural operations of divisive normalization, dynamic attraction, and delta rule learning respectively.