A Maximum Entropy Test for Evaluating Higher-Order Correlations in Spike Counts

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 spike count bin sizes at which the maximum entropy hypothesis can be rejected for a substantial number of neuronal pairs. These results demonstrate that higher-order correlations can matter when estimating information theoretic quantities in V1. They also show that our test is able to detect their presence in typical in-vivo data sets, where the number of samples is too small to estimate higher-order correlations directly. Author Summary: Populations of neurons signal information by their joint activity. Dependencies between the activity of multiple neurons are typically described by the linear correlation coefficient. However, this description of the dependencies is not complete. Dependencies beyond the linear correlation coefficient, so-called higher-order correlations, are often neglected because too many experimental samples are required in order to estimate them reliably. Evaluating the importance of higher-order correlations for the neural representation has therefore been notoriously hard. We devise a statistical test that can quantify evidence for higher-order correlations without estimating higher-order correlations directly. The test yields reliable results even when the number of experimental samples is small. The power of the method is demonstrated on data which were recorded from a population of neurons in the primary visual cortex of cat during an adaptation experiment. We show that higher-order correlations can have a substantial impact on the encoded stimulus information which, moreover, is modulated by stimulus adaptation.