# Logistic Variational Bayes Revisited

arXiv: https://arxiv.org/abs/2406.00713 · HTML: https://mlsanity.com/paper/2406.00713/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 12 of its 28 references that are in the map.
- First posted on arXiv 2 Jun 2024.

## Builds on (most cited first, 12 of 12)

- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Variational Inference: A Review for Statisticians](https://mlsanity.com/paper/1601.00670/) (2016)
- [GPyTorch: Blackbox Matrix-Matrix Gaussian Process Inference with GPU Acceleration](https://mlsanity.com/paper/1809.11165/) (2018)
- [New insights and perspectives on the natural gradient method](https://mlsanity.com/paper/1412.1193/) (2014)
- [Advances in Variational Inference](https://mlsanity.com/paper/1711.05597/) (2017)
- [Scalable Variational Gaussian Process Classification](https://mlsanity.com/paper/1411.2005/) (2014)
- [Scaling Hamiltonian Monte Carlo Inference for Bayesian Neural Networks with Symmetric Splitting](https://mlsanity.com/paper/2010.06772/) (2020)
- [Covariances, Robustness, and Variational Bayes](https://mlsanity.com/paper/1709.02536/) (2017)
- [Spike and slab variational Bayes for high dimensional logistic regression](https://mlsanity.com/paper/2010.11665/) (2020)
- [Bayesian Optimization with Binary Auxiliary Information](https://mlsanity.com/paper/1906.07277/) (2019)
- [Conditionally conjugate mean-field variational Bayes for logistic models](https://mlsanity.com/paper/1711.06999/) (2017)
- [Variational Bayes for high-dimensional proportional hazards models with applications within gene expression](https://mlsanity.com/paper/2112.10270/) (2021)

## Built on by (most cited first, 1 of 1)

- [Variational predictive resampling](https://mlsanity.com/paper/2605.11168/) (2026)

## Abstract (arXiv)

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.