a maximum entropy test for evaluating higher-order correlations in spike counts最大熵测试评估高阶相关性在飙升.pdfVIP

A Maximum Entropy Test for Evaluating Higher-Order Correlations in Spike Counts 1,2 3 1,2 Arno Onken *, Valentin Dragoi , Klaus Obermayer ¨ 1Technische Universitat Berlin, Berlin, Germany, 2 Bernstein Center for Computational Neuroscience Berlin, Berlin, Germany, 3 University of Texas, Houston Medical School, Houston, Texas, United States of America Abstract Evaluating the importance of higher-order correlations of neural spike counts has been notoriously hard. A large number of samples are typically required in order to estimate higher-order correlations and resulting information theoretic quantities. In typical electrophysiology data sets with many experimental conditions, however, the number of samples in each condition is rather small. Here we describe a method that allows to quantify evidence for higher-order correlations in exactly these cases. We construct a family of reference distributions: maximum entropy distributions, which are constrained only by marginals and by linear correlations as quantified by the Pearson correlation coefficient. We devise a Monte Carlo goodness- of-fit test, which tests - for a given divergence measure of interest - whether the experimental data lead to the rejection of the null hypothesis that it was generated by one of the reference distributions. Applying our test to artificial data shows that the effects of higher-order correlations on these divergence measures can be detected even when the number of samples is small. Subsequently, we apply our method to spike count data which were recorded with multielectrode arrays from the primary visual cortex of anesthetized cat during an adaptation experiment. Using mutual information as a divergence measure we find that there are