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A Comparison of Descriptive Models of a Single Spike Train by Information-Geometric Measure

hiro{at}brain.riken.jp.

Shun-ichi Amari

amari{at}brain.riken.go.jp Laboratory for Mathematical Neuroscience, RIKEN Brain Science Institute, Wako, Saitama, 351-0198 Japan

Barry J. Richmond

bjr{at}ln.nimh.nih.gov Laboratory of Neuropsychology, National Institute of Mental Health, National Institutes of Health, Bethesda, MD 20892, U.S.A.

In examining spike trains, different models are used to describe their structure. The different models often seem quite similar, but because they are cast in different formalisms, it is often difficult to compare their predictions. Here we use the information-geometric measure, an orthogonal coordinate representation of point processes, to express different models of stochastic point processes in a common coordinate system. Within such a framework, it becomes straightforward to visualize higher-order correlations of different models and thereby assess the differences between models. We apply the information-geometric measure to compare two similar but not identical models of neuronal spike trains: the inhomogeneous Markov and the mixture of Poisson models. It is shown that they differ in the second- and higher-order interaction terms. In the mixture of Poisson model, the second- and higher-order interactions are of comparable magnitude within each order, whereas in the inhomogeneous Markov model, they have alternating signs over different orders. This provides guidance about what measurements would effectively separate the two models. As newer models are proposed, they also can be compared to these models using information geometry.