Information Geometry of Multiple Spike Trains

Abstract

Information geometry studies a family probability distributions by using modern geometry. Since a stochastic model of multiple spike trains is described by a family of probability distributions, information geometry provides not only intuitive understanding, but also useful tools to analyze complex spike trains. A stochastic model of neuronal spikes represents average firing rates and correlations of spikes. We separate correlations of spikes from their firing rates orthogonally. We further separate higher-order correlations from lower-order ones, and thus the effect of correlations is decomposed orthogonally. However, a general model is too complicated and is not adequate for practical use. So we study characteristics of various tractable models. We study among them a mixture model, which is simple and tractable and has many interesting properties. We also study a marginal model and its characteristics.