  A restricted Boltzmann machine (RBM) is an undirected graphical model
constructed for discrete or continuous random variables, with two layers, one
hidden and one visible, and no conditional dependency within a layer. In recent
years, RBMs have risen to prominence due to their connection to deep learning.
By treating a hidden layer of one RBM as the visible layer in a second RBM, a
deep architecture can be created. RBMs are thought to thereby have the ability
to encode very complex and rich structures in data, making them attractive for
supervised learning. However, the generative behavior of RBMs is largely
unexplored and typical fitting methodology does not easily allow for
uncertainty quantification in addition to point estimates. In this paper, we
discuss the relationship between RBM parameter specification in the binary case
and model properties such as degeneracy, instability and uninterpretability. We
also describe the associated difficulties that can arise with likelihood-based
inference and further discuss the potential Bayes fitting of such (highly
flexible) models, especially as Gibbs sampling (quasi-Bayes) methods are often
advocated for the RBM model structure.
