Logistic Variational Bayes Revisited
This addresses the problem of costly or poor approximations in Bayesian inference for machine learning practitioners, though it is incremental as it builds on existing variational methods.
The paper tackles the intractability of the Evidence Lower Bound in variational logistic regression by introducing a new bound for the expectation of the softplus function, which leads to a variational posterior that achieves state-of-the-art performance and is significantly faster to compute than Monte-Carlo methods.
Variational logistic regression is a popular method for approximate Bayesian inference seeing wide-spread use in many areas of machine learning including: Bayesian optimization, reinforcement learning and multi-instance learning to name a few. However, due to the intractability of the Evidence Lower Bound, authors have turned to the use of Monte Carlo, quadrature or bounds to perform inference, methods which are costly or give poor approximations to the true posterior. In this paper we introduce a new bound for the expectation of softplus function and subsequently show how this can be applied to variational logistic regression and Gaussian process classification. Unlike other bounds, our proposal does not rely on extending the variational family, or introducing additional parameters to ensure the bound is tight. In fact, we show that this bound is tighter than the state-of-the-art, and that the resulting variational posterior achieves state-of-the-art performance, whilst being significantly faster to compute than Monte-Carlo methods.