mlsanityData to 13 Oct 2026

Conditional Bayesian Quadrature

arXiv 2406.16530 ↗First posted 24 Jun 2024stat.ML cs.LG stat.COcited by 8

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Abstract (arXiv)

We propose a novel approach for estimating conditional or parametric expectations in the setting where obtaining samples or evaluating integrands is costly. Through the framework of probabilistic numerical methods (such as Bayesian quadrature), our novel approach allows to incorporates prior information about the integrands especially the prior smoothness knowledge about the integrands and the conditional expectation. As a result, our approach provides a way of quantifying uncertainty and leads to a fast convergence rate, which is confirmed both theoretically and empirically on challenging tasks in Bayesian sensitivity analysis, computational finance and decision making under uncertainty.

Key facts. Cited by 8 papers in the map (data through 13 Oct 2026). Builds on 36 of its 97 references that are in the map. First posted on arXiv 24 Jun 2024.

Builds on

36 of 97 references.

References · 36

  1. 2017What Uncertainties Do We Need in Bayesian Deep Learning for Computer Vision?cited by 2,340
  2. 2016Kernel Mean Embedding of Distributions: A Review and Beyondcited by 360
  3. 2018Gaussian Processes and Kernel Methods: A Review on Connections and Equivalencescited by 190
  4. 2017On Nesting Monte Carlo Estimatorscited by 82
  5. 2015Probabilistic Numerics and Uncertainty in Computationscited by 59
  6. 2017Bayesian Probabilistic Numerical Methodscited by 50
  7. 2021Stein's Method Meets Computational Statistics: A Review of Some Recent Developmentscited by 32
  8. 2014Sampling for Inference in Probabilistic Models with Fast Bayesian Quadraturecited by 31
  9. 2020Convergence Guarantees for Gaussian Process Means With Misspecified Likelihoods and Smoothnesscited by 30
  10. 2015Probabilistic Integration: A Role in Statistical Computation?cited by 26
  11. 2021Deconditional Downscaling with Gaussian Processescited by 24
  12. 2019Convergence Guarantees for Adaptive Bayesian Quadrature Methodscited by 22
24 more
  1. 2018Variational Bayesian Monte Carlocited by 20
  2. 2022Fast Bayesian Inference with Batch Bayesian Quadrature via Kernel Recombinationcited by 20
  3. 2019A Modern Retrospective on Probabilistic Numericscited by 18
  4. 2019Active Multi-Information Source Bayesian Quadraturecited by 17
  5. 2023Sampling-based Nystr"om Approximation and Kernel Quadraturecited by 17
  6. 2014Kernel Mean Shrinkage Estimatorscited by 16
  7. 2017Convergence Analysis of Deterministic Kernel-Based Quadrature Rules in Misspecified Settingscited by 16
  8. 2018Bayesian Quadrature for Multiple Related Integralscited by 15
  9. 2023Optimally-Weighted Estimators of the Maximum Mean Discrepancy for Likelihood-Free Inferencecited by 13
  10. 2021Discrepancy-based Inference for Intractable Generative Models using Quasi-Monte Carlocited by 12
  11. 2021Vector-Valued Control Variatescited by 12
  12. 2023When is Importance Weighting Correction Needed for Covariate Shift Adaptation?cited by 12
  13. 2021ProbNum: Probabilistic Numerics in Pythoncited by 10
  14. 2016Active Uncertainty Calibration in Bayesian ODE Solverscited by 9
  15. 2018Symmetry Exploits for Bayesian Cubature Methodscited by 8
  16. 2022Multilevel Bayesian Quadraturecited by 8
  17. 2014Characteristic Kernels and Infinitely Divisible Distributionscited by 7
  18. 2021Detecting and diagnosing prior and likelihood sensitivity with power-scalingcited by 7
  19. 2023Meta-learning Control Variates: Variance Reduction with Limited Datacited by 6
  20. 2016Probabilistic Models for Integration Error in the Assessment of Functional Cardiac Modelscited by 5
  21. 2020Bayesian Probabilistic Numerical Integration with Tree-Based Modelscited by 5
  22. 2022Efficient estimation of multiple expectations with the same sample by adaptive importance sampling and control variatescited by 3
  23. 2023Bayesian Numerical Integration with Neural Networkscited by 3
  24. 2023Bayesian Quadrature for Neural Ensemble Searchcited by 1

Built on by

Cited by year (2026 to 13 Oct)

Citing papers per year: 2025: 5; 2026: 3.

8 papers.

  1. 2025A Dictionary of Closed-Form Kernel Mean Embeddingscited by 9
  2. 2025Nested Expectations with Kernel Quadraturecited by 5
  3. 2026Sobolev Regularized MMD Gradient Flowcited by 3
  4. 2025Stationary MMD Pointscited by 2
  5. 2025ActiveCQ: Active Estimation of Causal Quantitiescited by 1
  6. 2026Bayesian Quadraturecited by 1
  7. 2025BayesSum: Bayesian Quadrature in Discrete Spacescited by 0
  8. 2026A Gradient Flow Perspective on Minimum MMD Estimationcited by 0