# Learning Gaussian-Bernoulli RBMs using Difference of Convex Functions Optimization. (arXiv:2102.06228v1 [cs.LG])

The Gaussian-Bernoulli restricted Boltzmann machine (GB-RBM) is a useful
generative model that captures meaningful features from the given
$n$-dimensional continuous data. The difficulties associated with learning
GB-RBM are reported extensively in earlier studies. They indicate that the
training of the GB-RBM using the current standard algorithms, namely,
contrastive divergence (CD) and persistent contrastive divergence (PCD), needs
a carefully chosen small learning rate to avoid divergence which, in turn,
results in slow learning. In this work, we alleviate such difficulties by
showing that the negative log-likelihood for a GB-RBM can be expressed as a
difference of convex functions if we keep the variance of the conditional
distribution of visible units (given hidden unit states) and the biases of the
visible units, constant. Using this, we propose a stochastic {em difference of
convex functions} (DC) programming (S-DCP) algorithm for learning the GB-RBM.
We present extensive empirical studies on several benchmark datasets to
validate the performance of this S-DCP algorithm. It is seen that S-DCP is
better than the CD and PCD algorithms in terms of speed of learning and the
quality of the generative model learnt.