  Deep neural networks (DNNs) often require good regularizers to generalize
well. Currently, state-of-the-art DNN regularization techniques consist in
randomly dropping units and/or connections on each iteration of the training
algorithm. Dropout and DropConnect are characteristic examples of such
regularizers, that are widely popular among practitioners. However, a drawback
of such approaches consists in the fact that their postulated probability of
random unit/connection omission is a constant that must be heuristically
selected based on the obtained performance in some validation set. To alleviate
this burden, in this paper we regard the DNN regularization problem from a
Bayesian inference perspective: We impose a sparsity-inducing prior over the
network synaptic weights, where the sparsity is induced by a set of
Bernoulli-distributed binary variables with Beta (hyper-)priors over their
prior parameters. This way, we eventually allow for marginalizing over the DNN
synaptic connectivity for output generation, thus giving rise to an effective,
heuristics-free, network regularization scheme. We perform Bayesian inference
for the resulting hierarchical model by means of an efficient Black-Box
Variational inference scheme. We exhibit the advantages of our method over
existing approaches by conducting an extensive experimental evaluation using
benchmark datasets.
