Properties and Bayesian fitting of restricted Boltzmann machines
This work addresses challenges in generative modeling and uncertainty estimation for RBMs, which are incremental improvements for researchers in machine learning and statistics.
The paper tackles the problem of understanding and fitting restricted Boltzmann machines (RBMs) by analyzing their properties like degeneracy and instability in the binary case, and proposes Bayesian methods to address uncertainty quantification, though it does not report concrete numerical results.
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.