Topographic product models applied to natural scene statistics.

We present an energy-based model that uses a product of generalized Student-t distributions to capture the statistical structure in data sets. This model is inspired by and particularly applicable to "natural" data sets such as images. We begin by providing the mathematical framework, where we discuss complete and overcomplete models and provide algorithms for training these models from data. Using patches of natural scenes, we demonstrate that our approach represents a viable alternative to independent component analysis as an interpretive model of biological visual systems. Although the two approaches are similar in flavor, there are also important differences, particularly when the representations are overcomplete. By constraining the interactions within our model, we are also able to study the topographic organization of Gabor-like receptive fields that our model learns. Finally, we discuss the relation of our new approach to previous work--in particular, gaussian scale mixture models and variants of independent components analysis.