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A Moment-Based Maximum Entropy Model for Fitting Higher-Order Interactions in Neural Data

Department of Neuroscience, Physiology, and Pharmacology, University College London, London WC1E 6BT, UK
Department of Physiology and Biophysics, University of Colorado School of Medicine, Aurora, CO 80045, USA
Department of Applied Mathematics, University of Washington, Seattle, WA 98195, USA
Author to whom correspondence should be addressed.
Entropy 2018, 20(7), 489;
Received: 1 May 2018 / Revised: 15 June 2018 / Accepted: 19 June 2018 / Published: 23 June 2018
(This article belongs to the Special Issue Information Theory in Neuroscience)
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Correlations in neural activity have been demonstrated to have profound consequences for sensory encoding. To understand how neural populations represent stimulus information, it is therefore necessary to model how pairwise and higher-order spiking correlations between neurons contribute to the collective structure of population-wide spiking patterns. Maximum entropy models are an increasingly popular method for capturing collective neural activity by including successively higher-order interaction terms. However, incorporating higher-order interactions in these models is difficult in practice due to two factors. First, the number of parameters exponentially increases as higher orders are added. Second, because triplet (and higher) spiking events occur infrequently, estimates of higher-order statistics may be contaminated by sampling noise. To address this, we extend previous work on the Reliable Interaction class of models to develop a normalized variant that adaptively identifies the specific pairwise and higher-order moments that can be estimated from a given dataset for a specified confidence level. The resulting “Reliable Moment” model is able to capture cortical-like distributions of population spiking patterns. Finally, we show that, compared with the Reliable Interaction model, the Reliable Moment model infers fewer strong spurious higher-order interactions and is better able to predict the frequencies of previously unobserved spiking patterns. View Full-Text
Keywords: maximum entropy; higher-order correlations; neural population coding; Ising model maximum entropy; higher-order correlations; neural population coding; Ising model

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Cayco-Gajic, N.A.; Zylberberg, J.; Shea-Brown, E. A Moment-Based Maximum Entropy Model for Fitting Higher-Order Interactions in Neural Data. Entropy 2018, 20, 489.

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