# Nonlinear MCMC for Bayesian Machine Learning

arXiv: https://arxiv.org/abs/2202.05621 · HTML: https://mlsanity.com/paper/2202.05621/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 19 of its 78 references that are in the map.
- First posted on arXiv 11 Feb 2022.

## Builds on (most cited first, 19 of 19)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [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)
- [Variational Inference with Normalizing Flows](https://mlsanity.com/paper/1505.05770/) (2015)
- [Normalizing Flows for Probabilistic Modeling and Inference](https://mlsanity.com/paper/1912.02762/) (2019)
- [Black Box Variational Inference](https://mlsanity.com/paper/1401.0118/) (2013)
- [A Conceptual Introduction to Hamiltonian Monte Carlo](https://mlsanity.com/paper/1701.02434/) (2017)
- [Cyclical Stochastic Gradient MCMC for Bayesian Deep Learning](https://mlsanity.com/paper/1902.03932/) (2019)
- [High-dimensional Bayesian inference via the Unadjusted Langevin Algorithm](https://mlsanity.com/paper/1605.01559/) (2016)
- [Maximum Mean Discrepancy Gradient Flow](https://mlsanity.com/paper/1906.04370/) (2019)
- [Preconditioned Stochastic Gradient Langevin Dynamics for Deep Neural Networks](https://mlsanity.com/paper/1512.07666/) (2015)
- [Evaluating Uncertainty Quantification in End-to-End Autonomous Driving Control](https://mlsanity.com/paper/1811.06817/) (2018)
- [Resampling Base Distributions of Normalizing Flows](https://mlsanity.com/paper/2110.15828/) (2021)
- [Langevin-gradient parallel tempering for Bayesian neural learning](https://mlsanity.com/paper/1811.04343/) (2018)
- [Handling of uncertainty in medical data using machine learning and probability theory techniques: A review of 30 years (1991-2020)](https://mlsanity.com/paper/2008.10114/) (2020)
- [Interacting Particle Markov Chain Monte Carlo](https://mlsanity.com/paper/1602.05128/) (2016)
- [PDMP Monte Carlo methods for piecewise-smooth densities](https://mlsanity.com/paper/2111.05859/) (2021)
- [Capture Uncertainties in Deep Neural Networks for Safe Operation of Autonomous Driving Vehicles](https://mlsanity.com/paper/2108.05118/) (2021)
- [Collective Proposal Distributions for Nonlinear MCMC samplers: Mean-Field Theory and Fast Implementation](https://mlsanity.com/paper/1909.08988/) (2019)

## Built on by (most cited first, 2 of 2)

- [Learning Distributions via Monte-Carlo Marginalization](https://mlsanity.com/paper/2308.06352/) (2023)
- [Exploring Image Generation via Mutually Exclusive Probability Spaces and Local Correlation Hypothesis](https://mlsanity.com/paper/2506.21731/) (2025)

## Abstract (arXiv)

We explore the application of a nonlinear MCMC technique first introduced in [1] to problems in Bayesian machine learning. We provide a convergence guarantee in total variation that uses novel results for long-time convergence and large-particle ("propagation of chaos") convergence. We apply this nonlinear MCMC technique to sampling problems including a Bayesian neural network on CIFAR10.