Bayesian Online Natural Gradient (BONG)

TL;DR

This paper introduces BONG, a Bayesian online inference method that simplifies variational Bayes by focusing on expected log-likelihood and natural gradient updates, achieving exact inference for conjugate models and improved performance in neural network applications.

Contribution

BONG presents a novel online Bayesian inference approach that avoids the KL regularization term, enabling efficient and accurate updates, especially for non-conjugate models like neural networks.

Findings

Outperforms existing online VB methods in non-conjugate settings

Achieves exact Bayesian inference for conjugate models

Provides efficient deterministic approximations for Gaussian variational distributions

Abstract

We propose a novel approach to sequential Bayesian inference based on variational Bayes (VB). The key insight is that, in the online setting, we do not need to add the KL term to regularize to the prior (which comes from the posterior at the previous timestep); instead we can optimize just the expected log-likelihood, performing a single step of natural gradient descent starting at the prior predictive. We prove this method recovers exact Bayesian inference if the model is conjugate. We also show how to compute an efficient deterministic approximation to the VB objective, as well as our simplified objective, when the variational distribution is Gaussian or a sub-family, including the case of a diagonal plus low-rank precision matrix. We show empirically that our method outperforms other online VB methods in the non-conjugate setting, such as online learning for neural networks, especially when controlling for computational costs.