Natural image statistics: Energy-based models estimated by score matching

Score matching is recent framework for parameter estimation in energy based models. In this class of probabilistic models, the intractable partition function has classically made learning a computationally expensive process necessitating the use of approximations, but with score matching this is no longer the case. This makes it straightforward to estimate models of natural images that have an intractable partition function, but offer advantages over classical model such as ICA by allowing for overcompleteness or nonlinear representations. Here we present two such models for natural images. The first is a hierarchical model with two layers estimated from the data, where the second layer serves to capture variance dependencies between first layer outputs. The second model we consider is an extension of ICA to a Markov random field, which allows us to generalize the ICA framework to images of arbitrary size.