Stochastic Gradient Estimate Variance in Contrastive Divergence and Persistent Contrastive Divergence

Contrastive Divergence (CD) and Persistent Contrastive Divergence (PCD) are popular methods for training Restricted Boltzmann Machines. However, both methods use an approximate method for sampling from the model distribution. As a side effect, these approximations yield significantly different biases and variances for stochastic gradient estimates of individual data points. It is well known that CD yields a biased gradient estimate. In this paper we however show empirically that CD has a lower stochastic gradient estimate variance than unbiased sampling, while the mean of subsequent PCD estimates has a higher variance than independent sampling. The results give one explanation to the finding that CD can be used with smaller minibatches or higher learning rates than PCD.