Approximate Learning in Temporal Hidden Hopfield Models

Abstract

Many popular probabilistic models for temporal sequences assume simple hidden dynamics or low-dimensionality of discrete variables. For higher dimensional discrete hidden variables, recourse is often made to approximate mean field theories, which to date have been applied to models with only simple hidden unit dynamics. We consider a class of models in which the discrete hidden space is defined by parallel dynamics of densely connected high-dimensional stochastic Hopfield networks. For these Hidden Hopfield Models (HHMs), mean field methods are derived for learning discrete and continuous temporal sequences. We also discuss applications of HHMs to learning of incomplete sequences and reconstruction of 3D occupancy graphs.