mlsanityData to 7 Oct 2026

Robust Generalised Bayesian Inference for Intractable Likelihoods

arXiv 2104.07359 ↗First posted 15 Apr 2021stat.ME math.ST stat.COcited by 53

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Abstract (arXiv)

Generalised Bayesian inference updates prior beliefs using a loss function, rather than a likelihood, and can therefore be used to confer robustness against possible mis-specification of the likelihood. Here we consider generalised Bayesian inference with a Stein discrepancy as a loss function, motivated by applications in which the likelihood contains an intractable normalisation constant. In this context, the Stein discrepancy circumvents evaluation of the normalisation constant and produces generalised posteriors that are either closed form or accessible using standard Markov chain Monte Carlo. On a theoretical level, we show consistency, asymptotic normality, and bias-robustness of the generalised posterior, highlighting how these properties are impacted by the choice of Stein discrepancy. Then, we provide numerical experiments on a range of intractable distributions, including applications to kernel-based exponential family models and non-Gaussian graphical models.

Key facts. Cited by 53 papers in the map (data through 7 Oct 2026). Builds on 34 of its 111 references that are in the map. First posted on arXiv 15 Apr 2021.

Builds on

34 of 111 references.

References · 34

  1. 2015Automatic differentiation in machine learning: a surveycited by 846
  2. 2016A Kernelized Stein Discrepancy for Goodness-of-fit Tests and Model Evaluationcited by 236
  3. 2013A General Framework for Updating Belief Distributionscited by 172
  4. 2015A Complete Recipe for Stochastic Gradient MCMCcited by 146
  5. 2016A Kernel Test of Goodness of Fitcited by 143
  6. 2015On the properties of variational approximations of Gibbs posteriorscited by 121
  7. 2017Measuring Sample Quality with Kernelscited by 119
  8. 2015Measuring Sample Quality with Stein's Methodcited by 94
  9. 2014Inconsistency of Bayesian Inference for Misspecified Linear Models, and a Proposal for Repairing Itcited by 92
  10. 2019Generalized Variational Inference: Three arguments for deriving new Posteriorscited by 57
  11. 2019Minimum Stein Discrepancy Estimatorscited by 57
  12. 2017Assigning a value to a power likelihood in a general Bayesian modelcited by 46
22 more
  1. 2018Learning deep kernels for exponential family densitiescited by 36
  2. 2019MMD-Bayes: Robust Bayesian Estimation via Maximum Mean Discrepancycited by 35
  3. 2017General Bayesian Updating and the Loss-Likelihood Bootstrapcited by 34
  4. 2020Blindness of score-based methods to isolated components and mixing proportionscited by 33
  5. 2015Robust Bayesian inference via coarseningcited by 32
  6. 2019Stein Variational Gradient Descent With Matrix-Valued Kernelscited by 32
  7. 2020Stochastic Stein Discrepanciescited by 30
  8. 2019Stein Point Markov Chain Monte Carlocited by 29
  9. 2013On Graphical Models via Univariate Exponential Family Distributionscited by 26
  10. 2016Measuring Sample Quality with Diffusionscited by 25
  11. 2020Optimal Thinning of MCMC Outputcited by 25
  12. 2018Random Feature Stein Discrepanciescited by 23
  13. 2020Sliced Kernelized Stein Discrepancycited by 23
  14. 2020A comparison of learning rate selection methods in generalized Bayesian inferencecited by 23
  15. 2013On Russian Roulette Estimates for Bayesian Inference with Doubly-Intractable Likelihoodscited by 16
  16. 2015Gradient-free Hamiltonian Monte Carlo with Efficient Kernel Exponential Familiescited by 15
  17. 2017Objective Bayesian inference with proper scoring rulescited by 12
  18. 2018Fisher Efficient Inference of Intractable Modelscited by 9
  19. 2019Safe-Bayesian Generalized Linear Regressioncited by 9
  20. 2020Metropolis-Hastings with Averaged Acceptance Ratioscited by 6
  21. 2018Optimal shrinkage covariance matrix estimation under random sampling from elliptical distributionscited by 4
  22. 2020Robust and Efficient Approximate Bayesian Computation: A Minimum Distance Approachcited by 4

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Citing papers per year: 2021: 4; 2022: 6; 2023: 11; 2024: 13; 2025: 15; 2026: 4.

53 papers.

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  1. 2021Detecting Model Misspecification in Amortized Bayesian Inference with Neural Networkscited by 48
  2. 2022Robust Bayesian Inference for Simulator-based Models via the MMD Posterior Bootstrapcited by 41
  3. 2023A Rigorous Link between Deep Ensembles and (Variational) Bayesian Methodscited by 31
  4. 2021A Trust Crisis In Simulation-Based Inference? Your Posterior Approximations Can Be Unfaithfulcited by 27
  5. 2022Towards Reliable Simulation-Based Inference with Balanced Neural Ratio Estimationcited by 27
  6. 2024Addressing Misspecification in Simulation-based Inference through Data-driven Calibrationcited by 26
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  8. 2023Adversarial robustness of amortized Bayesian inferencecited by 17
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  10. 2021Composite Goodness-of-fit Tests with Kernelscited by 16
  11. 2023Robust and Scalable Bayesian Online Changepoint Detectioncited by 16
  12. 2021On the Robustness to Misspecification of α-Posteriors and Their Variational Approximationscited by 15
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  2. 2022Generalised Bayesian Inference for Discrete Intractable Likelihoodcited by 14
  3. 2023Robust and Conjugate Gaussian Process Regressioncited by 14
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  5. 2024Sourcerer: Sample-based Maximum Entropy Source Distribution Estimationcited by 9
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  7. 2025Simulation-based Bayesian inference under model misspecificationcited by 9
  8. 2025A Dictionary of Closed-Form Kernel Mean Embeddingscited by 9
  9. 2023Misspecification-robust Sequential Neural Likelihood for Simulation-based Inferencecited by 8
  10. 2024Detecting Model Misspecification in Amortized Bayesian Inference with Neural Networks: An Extended Investigationcited by 8
  11. 2024Concentration properties of fractional posterior in 1-bit matrix completioncited by 7
  12. 2024On the Robustness of Kernel Goodness-of-Fit Testscited by 7
  13. 2023Biological Sequence Kernels with Guaranteed Flexibilitycited by 6
  14. 2024A sparse PAC-Bayesian approach for high-dimensional quantile predictioncited by 6
  15. 2023Using Perturbation to Improve Goodness-of-Fit Tests based on Kernelized Stein Discrepancycited by 4
  16. 2025Scalable Valuation of Human Feedback through Provably Robust Model Alignmentcited by 4
  17. 2022A Fourier representation of kernel Stein discrepancy with application to Goodness-of-Fit tests for measures on infinite dimensional Hilbert spacescited by 3
  18. 2023PAC-Bayesian Soft Actor-Critic Learningcited by 3
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  21. 2025Decision Making under Model Misspecification: DRO with Robust Bayesian Ambiguity Setscited by 2
  22. 2025Robust inference using density-powered Stein operatorscited by 2
  23. 2024Adaptive posterior concentration rates for sparse high-dimensional linear regression with random design and unknown error variancecited by 1
  24. 2024Sequential Kernelized Stein Discrepancycited by 1
  25. 2025Federated Generalised Variational Inference: A Robust Probabilistic Federated Learning Frameworkcited by 1
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  27. 2025Inferring Optical Tissue Properties from Photoplethysmography using Hybrid Amortized Inferencecited by 1
  28. 2025Multi-Output Robust and Conjugate Gaussian Processescited by 1
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  30. 2026Outlier-robust Diffusion Posterior Sampling for Bayesian Inverse Problemscited by 1
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  32. 2026Generalised Robust Bayes for Joint Inference of Model and Contaminationcited by 1
  33. 2023Differentially Private Statistical Inference through β-Divergence One Posterior Samplingcited by 0
  34. 2023On the meaning of uncertainty for ethical AI: philosophy and practicecited by 0
  35. 2024Log-PDE Methods for Rough Signature Kernelscited by 0
  36. 2024Loss-based Bayesian Sequential Prediction of Value at Risk with a Long-Memory and Non-linear Realized Volatility Modelcited by 0
  37. 2025A recursive Bayesian neural network for constitutive modeling of sands under monotonic and cyclic loadingcited by 0
  38. 2025Correcting Mode Proportion Bias in Generalized Bayesian Inference via a Weighted Kernel Stein Discrepancycited by 0

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