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Soft Mixer Assignment in a Hierarchical Generative Model of Natural Scene Statistics

odelia{at}salk.edu Howard Hughes Medical Institute, Computational Neurobiology Lab, Salk Institute for Biological Studies, La Jolla, CA 92037, U.S.A.

Terrence J. Sejnowski

terry{at}salk.edu Howard Hughes Medical Institute, Computational Neurobiology Lab, Salk Institute for Biological Studies, La Jolla, CA 92037, and Department of Biology, University of California at San Diego, La Jolla, CA 92093, U.S.A.

Peter Dayan

dayan{at}gatsby.ucl.ac.uk Gatsby Computational Neuroscience Unit, University College, London WC1N 3AR, U.K.

Gaussian scale mixture models offer a top-down description of signal generation that captures key bottom-up statistical characteristics of filter responses to images. However, the pattern of dependence among the filters for this class of models is prespecified. We propose a novel extension to the gaussian scale mixture model that learns the pattern of dependence from observed inputs and thereby induces a hierarchical representation of these inputs. Specifically, we propose that inputs are generated by gaussian variables (modeling local filter structure), multiplied by a mixer variable that is assigned probabilistically to each input from a set of possible mixers. We demonstrate inference of both components of the generative model, for synthesized data and for different classes of natural images, such as a generic ensemble and faces. For natural images, the mixer variable assignments show invariances resembling those of complex cells in visual cortex; the statistics of the gaussian components of the model are in accord with the outputs of divisive normalization models. We also show how our model helps interrelate a wide range of models of image statistics and cortical processing.

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