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Estimating Information Rates with Confidence Intervals in Neural Spike Trains

shlens{at}salk.edu Salk Institute, La Jolla, CA 92037, and Institute for Nonlinear Science, University of California, San Diego, La Jolla, CA 92093, U.S.A.

Matthew B. Kennel

mkennel{at}ucsd.edu Institute for Nonlinear Science, University of California, San Diego, La Jolla, CA 92093, U.S.A.

Henry D. I. Abarbanel

habarbanel{at}ucsd.edu Institute for Nonlinear Science, University of California, San Diego, La Jolla, CA 92093, U.S.A., and Department of Physics and Marine Physical Laboratory, Scripps Institution of Oceanography, University of California, San Diego, La Jolla, CA 92093, U.S.A.

E. J. Chichilnisky

ej{at}salk.edu Salk Institute, La Jolla, CA 92037, U.S.A.

Information theory provides a natural set of statistics to quantify the amount of knowledge a neuron conveys about a stimulus. A related work (Kennel, Shlens, Abarbanel, & Chichilnisky, 2005) demonstrated how to reliably estimate, with a Bayesian confidence interval, the entropy rate from a discrete, observed time series. We extend this method to measure the rate of novel information that a neural spike train encodes about a stimulus—the average and specific mutual information rates. Our estimator makes few assumptions about the underlying neural dynamics, shows excellent performance in experimentally relevant regimes, and uniquely provides confidence intervals bounding the range of information rates compatible with the observed spike train. We validate this estimator with simulations of spike trains and highlight how stimulus parameters affect its convergence in bias and variance. Finally, we apply these ideas to a recording from a guinea pig retinal ganglion cell and compare results to a simple linear decoder.

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