On the importance of hidden bias and hidden entropy in representational efficiency of the Gaussian-Bipolar Restricted Boltzmann Machines

In this paper, we analyze the role of hidden bias in representational efficiency of the Gaussian-Bipolar Restricted Boltzmann Machines (GBPRBMs), which are similar to the widely used Gaussian-Bernoulli RBMs. Our experiments show that hidden bias plays an important role in shaping of the probability density function of the visible units. We define hidden entropy and propose it as a measure of representational efficiency of the model. By using this measure, we investigate the effect of hidden bias on the hidden entropy and provide a full analysis of the hidden entropy as function of the hidden bias for small models with up to three hidden units. We also provide an insight into understanding of the representational efficiency of the larger scale models. Furthermore, we introduce Normalized Empirical Hidden Entropy (NEHE) as an alternative to hidden entropy that can be computed for large models. Experiments on the MNIST, CIFAR-10 and Faces data sets show that NEHE can serve as measure of representational efficiency and gives an insight on minimum number of hidden units required to represent the data.