Restricted Boltzmann Machines are generative models that consist of a layer
of hidden variables connected to another layer of visible units, and they are
used to model the distribution over visible variables. In order to gain a
higher representability power, many hidden units are commonly used, which, in
combination with a large number of visible units, leads to a high number of
trainable parameters. In this work we introduce the Structural Restricted
Boltzmann Machine model, which taking advantage of the structure of the data in
hand, constrains connections of hidden units to subsets of visible units in
order to reduce significantly the number of trainable parameters, without
compromising performance. As a possible area of application, we focus on image
modelling. Based on the nature of the images, the structure of the connections
is given in terms of spatial neighbourhoods over the pixels of the image that
constitute the visible variables of the model. We conduct extensive experiments
on various image domains. Image denoising is evaluated with corrupted images
from the MNIST dataset. The generative power of our models is compared to
vanilla RBMs, as well as their classification performance, which is assessed
with five different image domains. Results show that our proposed model has a
faster and more stable training, while also obtaining better results compared
to an RBM with no constrained connections between its visible and hidden units.

本文介绍的结构受限玻尔兹曼机（Structural Restricted Boltzmann Machine）模型针对图像建模的应用，通过限制隐层单元与可见层子集的连接来显著降低可训练参数数量，而不会影响性能。通过对多个图像域进行广泛实验，评估使用 MNIST 数据集的图像去噪结果和五个不同图像域的分类性能，结果表明相比于无限制连接的 RBM，该模型具有更快、更稳定的训练，并且可以获得更好的结果。