On the optimization and pruning for Bayesian deep learning

TL;DR

This paper introduces an adaptive variational Bayesian method for neural networks that achieves high accuracy and effective pruning, combining MCMC and EM algorithms to improve Bayesian deep learning.

Contribution

It proposes a novel adaptive variational Bayesian algorithm with an EM-MCMC approach for efficient training and pruning of neural networks in Bayesian deep learning.

Findings

Achieves state-of-the-art performance on CIFAR-10, CIFAR-100, and ImageNet.

Effectively prunes neural networks while maintaining high accuracy.

Demonstrates the equivalence of the proposed method to SGHMC with preconditioning.

Abstract

The goal of Bayesian deep learning is to provide uncertainty quantification via the posterior distribution. However, exact inference over the weight space is computationally intractable due to the ultra-high dimensions of the neural network. Variational inference (VI) is a promising approach, but naive application on weight space does not scale well and often underperform on predictive accuracy. In this paper, we propose a new adaptive variational Bayesian algorithm to train neural networks on weight space that achieves high predictive accuracy. By showing that there is an equivalence to Stochastic Gradient Hamiltonian Monte Carlo(SGHMC) with preconditioning matrix, we then propose an MCMC within EM algorithm, which incorporates the spike-and-slab prior to capture the sparsity of the neural network. The EM-MCMC algorithm allows us to perform optimization and model pruning within one-shot. We evaluate our methods on CIFAR-10, CIFAR-100 and ImageNet datasets, and demonstrate that our dense model can reach the state-of-the-art performance and our sparse model perform very well compared to previously proposed pruning schemes.