  Bayesian approaches for learning deep neural networks (BNN) have been
received much attention and successfully applied to various applications.
Particularly, BNNs have the merit of having better generalization ability as
well as better uncertainty quantification. For the success of BNN, search an
appropriate architecture of the neural networks is an important task, and
various algorithms to find good sparse neural networks have been proposed. In
this paper, we propose a new node-sparse BNN model which has good theoretical
properties and is computationally feasible. We prove that the posterior
concentration rate to the true model is near minimax optimal and adaptive to
the smoothness of the true model. In particular the adaptiveness is the first
of its kind for node-sparse BNNs. In addition, we develop a novel MCMC
algorithm which makes the Bayesian inference of the node-sparse BNN model
feasible in practice.
