Structured Recurrent Temporal Restricted Boltzmann Machines.

The Recurrent temporal restricted Boltzmann machine (RTRBM) is a probabilistic model for temporal data, that has been shown to effectively capture both short and long-term dependencies in time-series. The topology of the RTRBM graphical model, however, assumes full connectivity between all the pairs of visible and hidden units, therefore ignoring the dependency structure between the different observations. Learning this structure has the potential to not only improve the prediction performance, but it can also reveal important patterns in the data. For example, given an econometric dataset, we could identify interesting dependencies between different market sectors; given a meteorological dataset, we could identify regional weather patterns. In this work we propose a new class of RTRBM, which explicitly uses a dependency graph to model the structure in the problem and to define the energy function. We refer to the new model as the structured RTRBM (SRTRBM). Our technique is related to methods such as graphical lasso, which are used to learn the topology of Gaussian graphical models. We also develop a spike-and-slab version of the RTRBM, and combine it with our method to learn structure in datasets with real valued observations. Our experimental results using synthetic and real datasets, demonstrate that the SRTRBM can improve the prediction performance of the RTRBM, particularly when the number of visible units is large and the size of the training set is small. It also reveals the structure underlying our benchmark datasets.