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.

本文提出了一种新的边界方法用于估计软加函数期望，并展示了它如何应用于变分逻辑回归和高斯过程分类。与其他边界方法不同，我们的方法不需要扩展变分族或引入额外的参数来确保边界的紧致性。实验证明，这个边界方法比现有方法更紧致，而且计算速度显著更快，从而获得了最先进的变分后验性能。

逻辑变分贝叶斯重新讨论