Finding neural codes using random projections

Abstract

A powerful approach to studying how information is transmitted in basic neural systems is based on finding stimulus–response classes that optimize the mutual information shared between the classes. The problem can be formally described in terms of finding a optimal quantization ( A, B) of a large discrete joint ( X, Y) distribution and various algorithms have been developed for this purpose. Recently, it has been proved that finding the optimal such quantization is NP-complete (optimal mutual information quantization is NP-complete, Neural information coding indicating that exact solutions may be computationally infeasible to find in some circumstances. We have developed a new randomized algorithm to solve the joint quantization problem. Under assumptions about the underlying ( X, Y) distribution, we prove that this algorithm converges to the “true” optimal quantization with high probability that can be increased by performing additional random trials.