Hierarchical Expectation Refinement for Learning Generative Perception Models

We present a class of generative models well suited to modeling perceptual processes and an algorithm for learning their parameters that promises to scale to learning very large models. The models are hierarchical, composed of multiple levels, and allow input only at the lowest level, the base of the hierarchy. Connections within a level are generally local and may or may not be directed. Connections between levels are directed and generally do not span multiple levels. The learning algorithm falls within the general family of expectation maximization algorithms. Parameter estimation proceeds level-by-level starting with components in the lowest level and moving up the hierarchy. Having learned the parameters for the components in a given level, those parameters are permanently fixed and are never revisited for the purposes of learning. These parameters do, however, play an important role in learning the parameters for higher-level components by helping to generate the samples used in subsequent parameter estimation. Within levels, learning is decomposed into many local subproblems suggesting a straightforward parallel implementation. The inference required for learning is carried out by local message passing and the arrangement of connections within the underlying networks is designed to facilitate this method of inference. Learning is unsupervised but can be easily adapted to accommodate labeled data. A prototype implementation is discussed along with some preliminary experimental results on a standard benchmark machine-learning data set.