  As data size and computing power increase, the architectures of deep neural
networks (DNNs) have been getting more complex and huge, and thus there is a
growing need to simplify such complex and huge DNNs. In this paper, we propose
a novel sparse Bayesian neural network (BNN) which searches a good DNN with an
appropriate complexity. We employ the masking variables at each node which can
turn off some nodes according to the posterior distribution to yield a nodewise
sparse DNN. We devise a prior distribution such that the posterior distribution
has theoretical optimalities (i.e. minimax optimality and adaptiveness), and
develop an efficient MCMC algorithm. By analyzing several benchmark datasets,
we illustrate that the proposed BNN performs well compared to other existing
methods in the sense that it discovers well condensed DNN architectures with
similar prediction accuracy and uncertainty quantification compared to large
DNNs.
