Inference by Reparameterization using Neural Population Codes
Vasudeva Raju, Rajkumar
Master of Science
Behavioral experiments on humans and animals suggest that the brain performs probabilistic inference to interpret its environment. Here we present a general-purpose, biologically plausible implementation of approximate inference based on Probabilistic Population Codes (PPCs). PPCs are distributed neural representations of probability distributions that are capable of implementing marginalization and cue-integration in a biologically plausible way. By connecting multiple PPCs together, we can naturally represent multivariate probability distributions, and capture the conditional dependency structure by setting those connections as in a probabilistic graphical model. To perform inference in general graphical models, one convenient and often accurate algorithm is Loopy Belief Propagation (LBP), a ‘message-passing’ algorithm that uses local marginalization and integration operations to perform approximate inference efficiently even for complex models. In LBP, a message from one node to a neighboring node is a function of incoming messages from all neighboring nodes, except the recipient. This exception renders it neurally implausible because neurons cannot readily send many different signals to many different target neurons. Interestingly, however, LBP can be reformulated as a sequence of Tree-based Re-Parameterization (TRP) updates on the graphical model which re-factorizes a portion of the probability distribution. Although this formulation still implicitly has the message exclusion problem, we show this can be circumvented by converting the algorithm to a nonlinear dynamical system with auxiliary variables and a separation of time-scales. By combining these ideas, we show that a network of PPCs can represent multivariate probability distributions and implement the TRP updates for the graphical model to perform probabilistic inference. Simulations with Gaussian graphical models demonstrate that the performance of the PPC-based neural network implementation of TRP updates for probabilistic inference is comparable to the direct evaluation of LBP, and thus provides a compelling substrate for general, probabilistic inference in the brain.
Probabilistic Inference; Probabilistic Population Codes; Tree-based Re-parameterization; neural network