Contrastive Divergence Learning May Diverge When Training Restricted Boltzmann Machines

Understanding and modeling how brains learn higher-level representations from sensory input is one of the key challenges in computational neuroscience and machine learning. Layered generative models such as deep belief networks (DBNs) are promising for unsupervised learning such representations, and new algorithms that operate in a layer-wise fashion make learning these models computationally tractable [1-5]. Restricted Boltzmann Machines (RBMs) are the typical building blocks for DBN layers. They are undirected graphical models, and their structure is a bipartite graph connecting input (visible) and hidden neurons. Training large undirected graphical models by likelihood maximization in general involves averages over an exponential number of terms, and obtaining unbiased estimates of these averages by Markov chain Monte Carlo methods typically requires many sampling steps. However …