  Learning attribute applicability of products in the Amazon catalog (e.g.,
predicting that a shoe should have a value for size, but not for battery-type
at scale is a challenge. The need for an interpretable model is contingent on
(1) the lack of ground truth training data, (2) the need to utilise prior
information about the underlying latent space and (3) the ability to understand
the quality of predictions on new, unseen data. To this end, we develop the
MaxMachine, a probabilistic latent variable model that learns distributed
binary representations, associated to sets of features that are likely to
co-occur in the data. Layers of MaxMachines can be stacked such that higher
layers encode more abstract information. Any set of variables can be clamped to
encode prior information. We develop fast sampling based posterior inference.
Preliminary results show that the model improves over the baseline in 17 out of
19 product groups and provides qualitatively reasonable predictions.
