mlsanityData to 14 Oct 2026

Approximate Inference for Fully Bayesian Gaussian Process Regression

arXiv 1912.13440 ↗First posted 31 Dec 2019stat.ML cs.LGcited by 31

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Abstract (arXiv)

Learning in Gaussian Process models occurs through the adaptation of hyperparameters of the mean and the covariance function. The classical approach entails maximizing the marginal likelihood yielding fixed point estimates (an approach called textitType II maximum likelihood or ML-II). An alternative learning procedure is to infer the posterior over hyperparameters in a hierarchical specification of GPs we call textitFully Bayesian Gaussian Process Regression (GPR). This work considers two approximation schemes for the intractable hyperparameter posterior: 1) Hamiltonian Monte Carlo (HMC) yielding a sampling-based approximation and 2) Variational Inference (VI) where the posterior over hyperparameters is approximated by a factorized Gaussian (mean-field) or a full-rank Gaussian accounting for correlations between hyperparameters. We analyze the predictive performance for fully Bayesian GPR on a range of benchmark data sets.

Key facts. Cited by 31 papers in the map (data through 14 Oct 2026). First posted on arXiv 31 Dec 2019.

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Citing papers per year: 2021: 3; 2022: 11; 2023: 9; 2024: 5; 2025: 3.

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  1. 2021The Promises and Pitfalls of Deep Kernel Learningcited by 81
  2. 2022Neural Diffusion Processescited by 50
  3. 2022Bayesian Active Learning with Fully Bayesian Gaussian Processescited by 26
  4. 2023Self-Correcting Bayesian Optimization through Bayesian Active Learningcited by 22
  5. 2024Sparse Inducing Points in Deep Gaussian Processes: Enhancing Modeling with Denoising Diffusion Variational Inferencecited by 16
  6. 2023Meta-learning Control Variates: Variance Reduction with Limited Datacited by 7
  7. 2023Adaptive Batch Sizes for Active Learning A Probabilistic Numerics Approachcited by 6
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  9. 2022Bayesian Optimisation for Active Monitoring of Air Pollutioncited by 5
  10. 2022Gaussian Process Surrogate Models for Neural Networkscited by 5
  11. 2022Phi-DVAE: Physics-Informed Dynamical Variational Autoencoders for Unstructured Data Assimilationcited by 5
  12. 2023Leveraging Locality and Robustness to Achieve Massively Scalable Gaussian Process Regressioncited by 5
19 more
  1. 2023Stochastic stiffness identification and response estimation of Timoshenko beams via physics-informed Gaussian processescited by 5
  2. 2022Fully Bayesian inference for latent variable Gaussian process modelscited by 4
  3. 2022Sparse Gaussian Process Hyperparameters: Optimize or Integrate?cited by 4
  4. 2023Physics-informed Gaussian process model for Euler-Bernoulli beam elementscited by 4
  5. 2024Fully Bayesian Differential Gaussian Processes through Stochastic Differential Equationscited by 4
  6. 2025BARK: A Fully Bayesian Tree Kernel for Black-box Optimizationcited by 3
  7. 2025Informed Initialization for Bayesian Optimization and Active Learningcited by 2
  8. 2023Stochastic Cell Transmission Models of Traffic Networkscited by 1
  9. 2023Data-driven Prior Learning for Bayesian Optimisationcited by 1
  10. 2021Validating Gaussian Process Models with Simulation-Based Calibrationcited by 0
  11. 2022A novel sampler for Gauss-Hermite determinantal point processes with application to Monte Carlo integrationcited by 0
  12. 2022A Bayesian Approach To Graph Partitioningcited by 0
  13. 2022The case for fully Bayesian optimisation in small-sample trialscited by 0
  14. 2022Scalable Bayesian Transformed Gaussian Processescited by 0
  15. 2023Applications of Gaussian Processes at Extreme Lengthscales: From Molecules to Black Holescited by 0
  16. 2024Transfer Learning Bayesian Optimization to Design Competitor DNA Molecules for Use in Diagnostic Assayscited by 0
  17. 2024Robust Inference of Dynamic Covariance Using Wishart Processes and Sequential Monte Carlocited by 0
  18. 2024Swine Diet Design using Multi-objective Regionalized Bayesian Optimizationcited by 0
  19. 2025BITS for GAPS: Bayesian Information-Theoretic Sampling for hierarchical GAussian Process Surrogatescited by 0