Mixed-Variate Restricted Boltzmann Machines

Restricted Boltzmann Machines (RBM) [9, 5] have recently attracted an increasing attention for their rich capacity in a variety of learning tasks, including multivariate distribution modelling, feature extraction, classification, and construction of deep architectures [8, 19]. An RBM is a two-layer Markov random field in which the visible layer represents observed variables and the hidden layer represents latent aspects of the data. Pairwise interactions are only permitted for units between layers. As a result, the posterior distribution over the hidden variables and the probability of the data generative model are easy to evaluate, allowing fast feature extraction and efficient sampling-based inference [7]. Nonetheless, most existing work in RBMs implicitly assumes that the visible layer contains variables of the same modality. By far the most popular input types are binary [5] and Gaussian [8]. Recent extension includes categorical [21], ordinal [25], Poisson [6] and Beta [13] data. To the best of our knowledge, none has been considered for multicategorical and category-ranking data, nor for a mixed combination of these data types. In this paper, we investigate a generalisation of the RBM for variables of multiple modalities and types.