Abstract

The recurrent temporal restricted Boltzmann machine (RTRBM) is a probabilistic time-series model. The topology of the RTRBM graphical model, however, assumes full connectivity between all the pairs of visible units and hidden units, thereby ignoring the dependency structure within the observations. Learning this structure has the potential for not only improving the prediction performance, but also revealing important dependency patterns in the data. For example, given a meteorological dataset, we could identify regional weather patterns. In this work, we propose a new class of RTRBM, which we refer to as the structured RTRBM (SRTRBM), which explicitly uses a graph to model the dependency structure. 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 the SRTRBM to learn dependency structures in datasets with real-valued observations. Our experimental results using synthetic and real datasets demonstrate that the SRTRBM can significantly 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 dependency structures underlying our benchmark datasets.