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A joint maximum-entropy model for binary neural population patterns and continuous signals

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http://pubman.mpdl.mpg.de/cone/persons/resource/persons83931

Gerwinn,  S
Research Group Computational Vision and Neuroscience, Max Planck Institute for Biological Cybernetics, Max Planck Society;
Department Empirical Inference, Max Planck Institute for Biological Cybernetics, Max Planck Society;

http://pubman.mpdl.mpg.de/cone/persons/resource/persons83801

Berens,  P
Research Group Computational Vision and Neuroscience, Max Planck Institute for Biological Cybernetics, Max Planck Society;

http://pubman.mpdl.mpg.de/cone/persons/resource/persons83805

Bethge,  M
Research Group Computational Vision and Neuroscience, Max Planck Institute for Biological Cybernetics, Max Planck Society;

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Gerwinn, S., Berens, P., & Bethge, M. (2010). A joint maximum-entropy model for binary neural population patterns and continuous signals. Advances in Neural Information Processing Systems 22: 23rd Annual Conference on Neural Information Processing Systems 2009, 620-628.


Cite as: http://hdl.handle.net/11858/00-001M-0000-0013-C0BE-0
Abstract
Second-order maximum-entropy models have recently gained much interest for describing the statistics of binary spike trains. Here, we extend this approach to take continuous stimuli into account as well. By constraining on the joint secondorder statistics, we obtain a joint Gaussian-Boltzmann distribution of continuous stimuli and binary neural firing patterns, for which we also compute marginal and conditional distributions. This model has the same computational complexity as pure binary models and fitting it to data is a convex problem. We show that the model can be seen as an extension to the classical spike-triggered average and can be used as a non-linear method for extracting features which a neural population is sensitive to. Further, by calculating the posterior distribution of stimuli given an observed neural response, the model can be used to decode stimuli and yields a natural spike-train metric. Therefore, extending the framework of maximumentropy models to continuous variables allows us to gain novel insights into the relationship between the firing patterns of neural ensembles and the stimuli they are processing.