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Secondorder maximumentropy 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 the joint secondorder statistics, we obtain a joint GaussianBoltzmann 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 spiketriggered average/covariance analysis and can be used as a nonlinear 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 spiketrain 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.
Author Information
Sebastian Gerwinn (MPI for Biological Cybernetics & University of Tübingen)
Philipp Berens (MPI for Biological Cybernetics & University of Tübingen)
Matthias Bethge (University Tübingen)
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2009 Spotlight: A joint maximumentropy model for binary neural population patterns and continuous signals »
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