Gaussian-binary restricted Boltzmann machines for modeling natural image statistics

We present a theoretical analysis of Gaussian-binary restricted Boltzmann machines (GRBMs) from the perspective of density models. The key aspect of this analysis is to show that GRBMs can be formulated as a constrained mixture of Gaussians, which gives a much better insight into the model’s capabilities and limitations. We further show that GRBMs are capable of learning meaningful features without using a regularization term and that the results are comparable to those of independent component analysis. This is illustrated for both a two-dimensional blind source separation task and for modeling natural image patches. Our findings exemplify that reported difficulties in training GRBMs are due to the failure of the training algorithm rather than the model itself. Based on our analysis we derive a better training setup and show empirically that it leads to faster and more robust training of GRBMs. Finally, we compare different sampling algorithms for training GRBMs and show that Contrastive Divergence performs better than training methods that use a persistent Markov chain.