Thurstonian Boltzmann Machines: Learning from Multiple Inequalities

Restricted Boltzmann machines (RBMs) have proved to be a versatile tool for a wide variety of machine learning tasks and as a building block for deep architectures [12, 24, 28]. The original proposals mainly handle binary visible and hidden units. Whilst binary hidden units are broadly applicable as feature detectors, non-binary visible data requires different designs. Recent extensions to other data types result in type-dependent models: the Gaussian for continuous inputs [12], Beta for bounded continuous inputs [16], Poisson for count data [9], multinomial for unordered categories [25], and ordinal models for ordered categories [37, 35]. The Boltzmann distribution permits several types to be jointly modelled, thus making the RBM a good tool for multimodal and complex social survey analysis. The work of [20, 29, 40] combines continuous (e.g., visual and audio) and discrete modalities (e.g., words). The work of [34] extends the idea further to incorporate ordinal and rank data. However, there are conceptual drawbacks: First, conditioned on the hidden layer, they are still separate type-specific models; second, handling ordered categories and ranks is not natural; and third, specifying direct correlation between these types remains difficult. The main thesis of this paper is that many data types can be captured in one unified model.