mlsanityData to 14 Oct 2026

Nonlinear MCMC for Bayesian Machine Learning

arXiv 2202.05621 ↗First posted 11 Feb 2022stat.ML cs.LG math.PRcited by 2

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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.

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

19 of 78 references.

References · 19

  1. 2015Deep Residual Learning for Image Recognitioncited by 52,096
  2. 2017On Calibration of Modern Neural Networkscited by 4,960
  3. 2015Dropout as a Bayesian Approximation: Representing Model Uncertainty in Deep Learningcited by 4,448
  4. 2015Variational Inference with Normalizing Flowscited by 2,170
  5. 2019Normalizing Flows for Probabilistic Modeling and Inferencecited by 1,323
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  7. 2017A Conceptual Introduction to Hamiltonian Monte Carlocited by 209
  8. 2019Cyclical Stochastic Gradient MCMC for Bayesian Deep Learningcited by 203
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  10. 2019Maximum Mean Discrepancy Gradient Flowcited by 127
  11. 2015Preconditioned Stochastic Gradient Langevin Dynamics for Deep Neural Networkscited by 121
  12. 2018Evaluating Uncertainty Quantification in End-to-End Autonomous Driving Controlcited by 55
7 more
  1. 2021Resampling Base Distributions of Normalizing Flowscited by 42
  2. 2018Langevin-gradient parallel tempering for Bayesian neural learningcited by 14
  3. 2020Handling of uncertainty in medical data using machine learning and probability theory techniques: A review of 30 years (1991-2020)cited by 12
  4. 2016Interacting Particle Markov Chain Monte Carlocited by 6
  5. 2021PDMP Monte Carlo methods for piecewise-smooth densitiescited by 5
  6. 2021Capture Uncertainties in Deep Neural Networks for Safe Operation of Autonomous Driving Vehiclescited by 3
  7. 2019Collective Proposal Distributions for Nonlinear MCMC samplers: Mean-Field Theory and Fast Implementationcited by 2

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Citing papers per year: 2023: 1; 2024: 0; 2025: 1.

2 papers.

  1. 2023Learning Distributions via Monte-Carlo Marginalizationcited by 4
  2. 2025Exploring Image Generation via Mutually Exclusive Probability Spaces and Local Correlation Hypothesiscited by 0