title: Soft mixer assignment in a hierarchical generative model of natural scene statistics.
abstract: 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.
authors.affiliation: Howard Hughes Medical Institute, Computational Neurobiology Lab, Salk Institute for Biological Studies, La Jolla, CA 92037, USA. odelia@salk.edu
authors.forename: Odelia
authors.initials: O
authors.lastname: Schwartz
authors.forename: Terrence J
authors.initials: TJ
authors.lastname: Sejnowski
authors.forename: Peter
authors.initials: P
authors.lastname: Dayan
mesh_terms: D000818:Animals; D006801:Humans; D008959:Models, Neurological; D015233:Models, Statistical; D019368:Nature; D016571:Neural Networks, Computer; D017711:Nonlinear Dynamics; D014785:Vision, Ocular / Q000502:physiology; D014795:Visual Pathways / Q000502:physiology*