Barriers and Dynamical Paths in Alternating Gibbs Sampling of Restricted Boltzmann Machines
This work addresses sampling efficiency in RBMs, an incremental improvement for unsupervised learning and statistical modeling applications.
The study found that standard Alternating Gibbs Sampling (AGS) in Restricted Boltzmann Machines is no more efficient than Metropolis-Hastings sampling on the data layer, but combining Gibbs sampling with Metropolis-Hastings in the latent space can improve performance when hidden units encode weakly dependent features, as demonstrated on Bars and Stripes, MNIST, and Lattice Proteins datasets.
Restricted Boltzmann Machines (RBM) are bi-layer neural networks used for the unsupervised learning of model distributions from data. The bipartite architecture of RBM naturally defines an elegant sampling procedure, called Alternating Gibbs Sampling (AGS), where the configurations of the latent-variable layer are sampled conditional to the data-variable layer, and vice versa. We study here the performance of AGS on several analytically tractable models borrowed from statistical mechanics. We show that standard AGS is not more efficient than classical Metropolis-Hastings (MH) sampling of the effective energy landscape defined on the data layer. However, RBM can identify meaningful representations of training data in their latent space. Furthermore, using these representations and combining Gibbs sampling with the MH algorithm in the latent space can enhance the sampling performance of the RBM when the hidden units encode weakly dependent features of the data. We illustrate our findings on three datasets: Bars and Stripes and MNIST, well known in machine learning, and the so-called Lattice Proteins, introduced in theoretical biology to study the sequence-to-structure mapping in proteins.