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11 Neural Models of Bayesian Belief Propagation

Animals are constantly faced with the challenge of interpreting signals from noisy sensors and acting in the face of incomplete knowledge about the environment. A rigorous approach to handling uncertainty is to characterize and process information using probabilities. Having estimates of the probabilities of objects and events allows one to make intelligent decisions in the presence of uncertainty. A prey could decide whether to keep foraging or to flee based on the probability that an observed movement or sound was caused by a predator. Probabilistic estimates are also essential ingredients of more sophisticated decision-making routines such as those based on expected reward or utility. An important component of a probabilistic system is a method for reasoning based on combining prior knowledge about the world with current input data. Such methods are typically based on some form of Bayesian inference, involving the computation of the posterior probability distribution of one or more random variables of interest given input data. In this chapter, we describe how neural circuits could implement a general algorithm for Bayesian inference known as belief propagation. The belief propagation algorithm involves passing " messages " (probabilities) between the nodes of a graphical model that captures the causal structure of the environment. We review the basic notion of graphical models and illustrate the belief propagation algorithm with an example. We investigate potential neural implementations of the algorithm based on networks of leaky integrator neu-rons and describe how such networks can perform sequential and hierarchical Bayesian inference. Simulation results are presented for comparison with neu-robiological data. We conclude the chapter by discussing other recent models of inference in neural circuits and suggest directions for future research. Some of the ideas reviewed in this chapter have appeared in prior publications [30, 31, 32, 42]; these may be consulted for additional details and results not included in this chapter.