Sampling from Bayesian Neural Network Posteriors with Symmetric Minibatch Splitting Langevin Dynamics
This work addresses the problem of efficient and accurate posterior sampling in Bayesian neural networks for researchers and practitioners in machine learning, offering an incremental improvement over existing sampling techniques.
The authors tackled the challenge of sampling from Bayesian neural network posteriors by proposing a scalable kinetic Langevin dynamics algorithm with symmetric minibatch splitting, achieving bias control of O(h^2 d^{1/2}) and demonstrating significantly better calibration performance on datasets like Fashion-MNIST, Celeb-A, and chest X-ray compared to standard methods.
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.