Efficient Bayes Inference in Neural Networks through Adaptive Importance Sampling

TL;DR

This paper introduces PMCnet, an adaptive importance sampling algorithm that efficiently approximates the posterior distribution in Bayesian neural networks, enhancing exploration and reducing computational costs.

Contribution

The paper presents a novel adaptive importance sampling algorithm, PMCnet, tailored for Bayesian neural networks, improving posterior estimation and exploration capabilities.

Findings

PMCnet outperforms existing methods in accuracy and efficiency.

Enhanced exploration of complex, multimodal posteriors.

Effective in both shallow and deep neural network models.

Abstract

Bayesian neural networks (BNNs) have received an increased interest in the last years. In BNNs, a complete posterior distribution of the unknown weight and bias parameters of the network is produced during the training stage. This probabilistic estimation offers several advantages with respect to point-wise estimates, in particular, the ability to provide uncertainty quantification when predicting new data. This feature inherent to the Bayesian paradigm, is useful in countless machine learning applications. It is particularly appealing in areas where decision-making has a crucial impact, such as medical healthcare or autonomous driving. The main challenge of BNNs is the computational cost of the training procedure since Bayesian techniques often face a severe curse of dimensionality. Adaptive importance sampling (AIS) is one of the most prominent Monte Carlo methodologies benefiting from sounded convergence guarantees and ease for adaptation. This work aims to show that AIS constitutes a successful approach for designing BNNs. More precisely, we propose a novel algorithm PMCnet that includes an efficient adaptation mechanism, exploiting geometric information on the complex (often multimodal) posterior distribution. Numerical results illustrate the excellent performance and the improved exploration capabilities of the proposed method for both shallow and deep neural networks.