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 ex...

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Main Authors:	Onken, Arno, Dragoi, Valentin, Obermayer, Klaus
Format:	Online
Language:	English
Published:	Public Library of Science 2012
Online Access:	https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3369943/

id	pubmed-3369943
recordtype	oai_dc
spelling	pubmed-33699432012-06-08 A Maximum Entropy Test for Evaluating Higher-Order Correlations in Spike Counts Onken, Arno Dragoi, Valentin Obermayer, Klaus Research Article 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. Public Library of Science 2012-06-07 /pmc/articles/PMC3369943/ /pubmed/22685392 http://dx.doi.org/10.1371/journal.pcbi.1002539 Text en Onken et al. http://creativecommons.org/licenses/by/4.0/ This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are properly credited.
repository_type	Open Access Journal
institution_category	Foreign Institution
institution	US National Center for Biotechnology Information
building	NCBI PubMed
collection	Online Access
language	English
format	Online
author	Onken, Arno Dragoi, Valentin Obermayer, Klaus
spellingShingle	Onken, Arno Dragoi, Valentin Obermayer, Klaus A Maximum Entropy Test for Evaluating Higher-Order Correlations in Spike Counts
author_facet	Onken, Arno Dragoi, Valentin Obermayer, Klaus
author_sort	Onken, Arno
title	A Maximum Entropy Test for Evaluating Higher-Order Correlations in Spike Counts
title_short	A Maximum Entropy Test for Evaluating Higher-Order Correlations in Spike Counts
title_full	A Maximum Entropy Test for Evaluating Higher-Order Correlations in Spike Counts
title_fullStr	A Maximum Entropy Test for Evaluating Higher-Order Correlations in Spike Counts
title_full_unstemmed	A Maximum Entropy Test for Evaluating Higher-Order Correlations in Spike Counts
title_sort	maximum entropy test for evaluating higher-order correlations in spike counts
description	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.
publisher	Public Library of Science
publishDate	2012
url	https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3369943/
_version_	1611535346577702912

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

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