# Affine Invariant Ensemble Transform Methods to Improve Predictive Uncertainty in Neural Networks

arXiv: https://arxiv.org/abs/2309.04742 · HTML: https://mlsanity.com/paper/2309.04742/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 16 of its 50 references that are in the map.
- First posted on arXiv 9 Sep 2023.

## Builds on (most cited first, 16 of 16)

- [On Calibration of Modern Neural Networks](https://mlsanity.com/paper/1706.04599/) (2017)
- [Dropout as a Bayesian Approximation: Representing Model Uncertainty in Deep Learning](https://mlsanity.com/paper/1506.02142/) (2015)
- [Simple and Scalable Predictive Uncertainty Estimation using Deep Ensembles](https://mlsanity.com/paper/1612.01474/) (2016)
- [Enhancing The Reliability of Out-of-distribution Image Detection in Neural Networks](https://mlsanity.com/paper/1706.02690/) (2017)
- [Can You Trust Your Model's Uncertainty? Evaluating Predictive Uncertainty Under Dataset Shift](https://mlsanity.com/paper/1906.02530/) (2019)
- [A Review of Uncertainty Quantification in Deep Learning: Techniques, Applications and Challenges](https://mlsanity.com/paper/2011.06225/) (2020)
- [Weight Uncertainty in Neural Networks](https://mlsanity.com/paper/1505.05424/) (2015)
- [Why ReLU networks yield high-confidence predictions far away from the training data and how to mitigate the problem](https://mlsanity.com/paper/1812.05720/) (2018)
- [Scalable Bayesian Optimization Using Deep Neural Networks](https://mlsanity.com/paper/1502.05700/) (2015)
- [Being Bayesian, Even Just a Bit, Fixes Overconfidence in ReLU Networks](https://mlsanity.com/paper/2002.10118/) (2020)
- [Noisy Natural Gradient as Variational Inference](https://mlsanity.com/paper/1712.02390/) (2017)
- [Bayesian Deep Learning via Subnetwork Inference](https://mlsanity.com/paper/2010.14689/) (2020)
- [The Case for Bayesian Deep Learning](https://mlsanity.com/paper/2001.10995/) (2020)
- [Do Bayesian Neural Networks Need To Be Fully Stochastic?](https://mlsanity.com/paper/2211.06291/) (2022)
- [Ensemble Kalman Inversion: A Derivative-Free Technique For Machine Learning Tasks](https://mlsanity.com/paper/1808.03620/) (2018)
- [Never look back - A modified EnKF method and its application to the training of neural networks without back propagation](https://mlsanity.com/paper/1805.08034/) (2018)

## Abstract (arXiv)

We consider the problem of performing Bayesian inference for logistic regression using appropriate extensions of the ensemble Kalman filter. Two interacting particle systems are proposed that sample from an approximate posterior and prove quantitative convergence rates of these interacting particle systems to their mean-field limit as the number of particles tends to infinity. Furthermore, we apply these techniques and examine their effectiveness as methods of Bayesian approximation for quantifying predictive uncertainty in neural networks.