Sampling from Bayesian Neural Network Posteriors with Symmetric Minibatch Splitting Langevin Dynamics

TL;DR

This paper introduces a scalable Langevin dynamics algorithm, SMS-UBU, for sampling Bayesian neural network posteriors, demonstrating improved calibration in classification tasks on multiple datasets.

Contribution

The paper presents a novel symmetric minibatch splitting Langevin dynamics method with controlled bias, enhancing sampling efficiency for large-scale Bayesian neural networks.

Findings

SMS-UBU achieves bias $O(h^2 d^{1/2})$ with only one minibatch per iteration.

BNNs sampled with SMS-UBU show better calibration than standard training methods.

The method is effective on datasets like Fashion-MNIST, Celeb-A, and chest X-ray.

Abstract

We propose a scalable kinetic Langevin dynamics algorithm for sampling parameter spaces of big data and AI applications. Our scheme combines a symmetric forward/backward sweep over minibatches with a symmetric discretization of Langevin dynamics. For a particular Langevin splitting method (UBU), we show that the resulting Symmetric Minibatch Splitting-UBU (SMS-UBU) integrator has bias $O(h^2 d^{1/2})$ in dimension $d>0$ with stepsize $h>0$, despite only using one minibatch per iteration, thus providing excellent control of the sampling bias as a function of the stepsize. We apply the algorithm to explore local modes of the posterior distribution of Bayesian neural networks (BNNs) and evaluate the calibration performance of the posterior predictive probabilities for neural networks with convolutional neural network architectures for classification problems on three different datasets (Fashion-MNIST, Celeb-A and chest X-ray). Our results indicate that BNNs sampled with SMS-UBU can offer significantly better calibration performance compared to standard methods of training and stochastic weight averaging.