mlsanityData to 7 Oct 2026

Fast Bayesian Inference with Batch Bayesian Quadrature via Kernel Recombination

arXiv 2206.04734 ↗First posted 9 Jun 2022cs.LG cs.NA math.NAcited by 20

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Abstract (arXiv)

Calculation of Bayesian posteriors and model evidences typically requires numerical integration. Bayesian quadrature (BQ), a surrogate-model-based approach to numerical integration, is capable of superb sample efficiency, but its lack of parallelisation has hindered its practical applications. In this work, we propose a parallelised (batch) BQ method, employing techniques from kernel quadrature, that possesses an empirically exponential convergence rate. Additionally, just as with Nested Sampling, our method permits simultaneous inference of both posteriors and model evidence. Samples from our BQ surrogate model are re-selected to give a sparse set of samples, via a kernel recombination algorithm, requiring negligible additional time to increase the batch size. Empirically, we find that our approach significantly outperforms the sampling efficiency of both state-of-the-art BQ techniques and Nested Sampling in various real-world datasets, including lithium-ion battery analytics.

Key facts. Cited by 20 papers in the map (data through 7 Oct 2026). Builds on 32 of its 103 references that are in the map. First posted on arXiv 9 Jun 2022.

Builds on

32 of 103 references.

References · 32

  1. 2018GPyTorch: Blackbox Matrix-Matrix Gaussian Process Inference with GPU Accelerationcited by 603
  2. 2019The frontier of simulation-based inferencecited by 490
  3. 2019Automatic Posterior Transformation for Likelihood-Free Inferencecited by 216
  4. 2015On the Equivalence between Kernel Quadrature Rules and Random Feature Expansionscited by 136
  5. 2018Maximizing acquisition functions for Bayesian optimizationcited by 113
  6. 2019Bayesian Batch Active Learning as Sparse Subset Approximationcited by 68
  7. 2015Bayesian Optimization for Likelihood-Free Inference of Simulator-Based Statistical Modelscited by 61
  8. 2014Control functionals for Monte Carlo integrationcited by 59
  9. 2015Probabilistic Numerics and Uncertainty in Computationscited by 59
  10. 2017Automated Scalable Bayesian Inference via Hilbert Coresetscited by 55
  11. 2016Batched Gaussian Process Bandit Optimization via Determinantal Point Processescited by 33
  12. 2014Sampling for Inference in Probabilistic Models with Fast Bayesian Quadraturecited by 31
20 more
  1. 2016A Multi-Batch L-BFGS Method for Machine Learningcited by 30
  2. 2019Sparse Variational Inference: Bayesian Coresets from Scratchcited by 28
  3. 2019Kernel quadrature with DPPscited by 26
  4. 2021Positively Weighted Kernel Quadrature via Subsamplingcited by 25
  5. 2020Variational Bayesian Monte Carlo with Noisy Likelihoodscited by 23
  6. 2019Convergence Guarantees for Adaptive Bayesian Quadrature Methodscited by 22
  7. 2015Frank-Wolfe Bayesian Quadrature: Probabilistic Integration with Theoretical Guaranteescited by 20
  8. 2018Variational Bayesian Monte Carlocited by 20
  9. 2017Dynamic nested sampling: an improved algorithm for parameter estimation and evidence calculationcited by 15
  10. 2018Improving Quadrature for Constrained Integrandscited by 12
  11. 2021Predicting battery end of life from solar off-grid system field data using machine learningcited by 8
  12. 2018Batch Selection for Parallelisation of Bayesian Quadraturecited by 6
  13. 2020Bayesian Parameter Estimation Applied to the Li-ion Battery Single Particle Model with Electrolyte Dynamicscited by 6
  14. 2020A Randomized Algorithm to Reduce the Support of Discrete Measurescited by 6
  15. 2017Identifiability and parameter estimation of the single particle lithium-ion battery modelcited by 5
  16. 2019Automated Model Selection with Bayesian Quadraturecited by 5
  17. 2021Bayesian Quadrature on Riemannian Data Manifoldscited by 5
  18. 2017Collaborative Nested Sampling: Big Data vs. complex physical modelscited by 4
  19. 2021Marginalising over Stationary Kernels with Bayesian Quadraturecited by 4
  20. 2015Lithium-ion battery thermal-electrochemical model-based state estimation using orthogonal collocation and a modified extended Kalman filtercited by 3

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2022: 1; 2023: 9; 2024: 3; 2025: 4; 2026: 3.

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  1. 2023Looping in the Human Collaborative and Explainable Bayesian Optimizationcited by 27
  2. 2023Sampling-based Nystr"om Approximation and Kernel Quadraturecited by 17
  3. 2022Bayesian Model Selection of Lithium-Ion Battery Models via Bayesian Quadraturecited by 8
  4. 2024Conditional Bayesian Quadraturecited by 8
  5. 2023SOBER: Highly Parallel Bayesian Optimization and Bayesian Quadrature over Discrete and Mixed Spacescited by 7
  6. 2023Machine Learning Benchmarks for the Classification of Equivalent Circuit Models from Electrochemical Impedance Spectracited by 7
  7. 2023Adaptive Batch Sizes for Active Learning A Probabilistic Numerics Approachcited by 6
  8. 2024Principled Bayesian Optimisation in Collaboration with Human Expertscited by 5
  9. 2023Fast post-process Bayesian inference with Variational Sparse Bayesian Quadraturecited by 3
  10. 2024A Quadrature Approach for General-Purpose Batch Bayesian Optimization via Probabilistic Liftingcited by 3
  11. 2025BioBO: Biology-informed Bayesian Optimization for Perturbation Designcited by 2
  12. 2023Bayesian Quadrature for Neural Ensemble Searchcited by 1
8 more
  1. 2023Compressed online Sinkhorncited by 1
  2. 2023Policy Gradient with Kernel Quadraturecited by 1
  3. 2025Normalizing Flow Regression for Bayesian Inference with Offline Likelihood Evaluationscited by 1
  4. 2025Natural Evolutionary Search meets Probabilistic Numericscited by 1
  5. 2026Bayesian Quadraturecited by 1
  6. 2025Measuring the right thing: justifying metrics in AI impact assessmentscited by 0
  7. 2026Convex-Geometric Error Bounds for Positive-Weight Kernel Quadraturecited by 0
  8. 2026Hierarchical Bayesian Quadraturecited by 0