An Empirical Investigation of Minimum Probability Flow Learning Under Different Connectivity Patterns

Energy-based models are popular in machine learning due to the elegance of their formulation and their relationship to statistical physics. Among these, the Restricted Boltzmann Machine (RBM), and its staple training algorithm contrastive divergence (CD), have been the prototype for some recent advancements in the unsupervised training of deep neural networks. However, CD has limited theoretical motivation, and can in some cases produce undesirable behaviour. Here, we investigate the performance of Minimum Probability Flow (MPF) learning for training RBMs. Unlike CD, with its focus on approximating an intractable partition function via Gibbs sampling, MPF proposes a tractable, consistent, objective function defined in terms of a Taylor expansion of the KL divergence with respect to sampling dynamics. Here we propose a more general form for the sampling dynamics in MPF, and explore the consequences of different choices for these dynamics for training RBMs. Experimental results show MPF outperforming CD for various RBM configurations.