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Restricted Boltzmann Machines are generative models that consist of a layerof hidden variables connected to another layer of visible units, and they areused to model the distribution over visible variables. In order to gain ahigher representability power, many hidden units are commonly used, which, incombination with a large number of visible units, leads to a high number oftrainable parameters. In this work we introduce the Structural RestrictedBoltzmann Machine model, which taking advantage of the structure of the data inhand, constrains connections of hidden units to subsets of visible units inorder to reduce significantly the number of trainable parameters, withoutcompromising performance. As a possible area of application, we focus on imagemodelling. Based on the nature of the images, the structure of the connectionsis given in terms of spatial neighbourhoods over the pixels of the image thatconstitute the visible variables of the model. We conduct extensive experimentson various image domains. Image denoising is evaluated with corrupted imagesfrom the MNIST dataset. The generative power of our models is compared tovanilla RBMs, as well as their classification performance, which is assessedwith five different image domains. Results show that our proposed model has afaster and more stable training, while also obtaining better results comparedto an RBM with no constrained connections between its visible and hidden units.

Structural Restricted Boltzmann Machine for image denoising and classification