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Soft Mixer Assignment in a Hierarchical Model of Natural Scene Statistics.
Odelia Schwartz, Terrence J. Sejnowski, and Peter Dayan.
Neural
Computation, 2006.
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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 amongst the
filters for this class of models is pre-specified. 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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