Logistic Variational Bayes Revisited

TL;DR

This paper introduces a new, tighter bound for variational logistic regression that improves accuracy and speed, avoiding complex extensions or additional parameters, and demonstrating state-of-the-art performance.

Contribution

A novel bound for the expectation of the softplus function that enhances variational logistic regression without increasing model complexity.

Findings

The new bound is tighter than existing bounds.

The proposed method achieves state-of-the-art performance.

It is significantly faster than Monte Carlo methods.

Abstract

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.