Information Geometry of Multiple Spike Trains
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.
KeywordsEntropy Manifold Covariance Dinates
Unable to display preview. Download preview PDF.
- Amari S (2009b) α-Divergence is unique, belonging to both f-divergence and Bregman divergence class. IEEE Transactions on Information Theory 55:November Google Scholar
- Amari S, Nagaoka H (2000) Methods of information geometry. Translations of mathematical monographs, vol 191. AMS & Oxford University Press, Providence Google Scholar
- Chentsov NN (1972) Statistical decision rules and optimal inference. American Mathematical Society, Providence 1982. Originally published in Russian, Nauka, Moscow Google Scholar
- Dayan P, Abbott LF (2005) Theoretical neuroscience: computational and mathematical modeling of neural systems. MIT Press, Cambridge Google Scholar
- Godambe VP (1991) Estimating functions. Oxford University Press, London Google Scholar
- Simazaki H, Gruen S, Amari S (2010) Analysis of subsets of higher-order correlated neurons based on marginal correlation coordinates. Cosyne 10 Google Scholar