  We introduce Thurstonian Boltzmann Machines (TBM), a unified architecture
that can naturally incorporate a wide range of data inputs at the same time.
Our motivation rests in the Thurstonian view that many discrete data types can
be considered as being generated from a subset of underlying latent continuous
variables, and in the observation that each realisation of a discrete type
imposes certain inequalities on those variables. Thus learning and inference in
TBM reduce to making sense of a set of inequalities. Our proposed TBM naturally
supports the following types: Gaussian, intervals, censored, binary,
categorical, muticategorical, ordinal, (in)-complete rank with and without
ties. We demonstrate the versatility and capacity of the proposed model on
three applications of very different natures; namely handwritten digit
recognition, collaborative filtering and complex social survey analysis.
