# Convergence Guarantees for Gaussian Process Means With Misspecified Likelihoods and Smoothness

arXiv: https://arxiv.org/abs/2001.10818 · HTML: https://mlsanity.com/paper/2001.10818/

## Key facts

- Cited by 30 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 29 Jan 2020.

## Built on by (most cited first, 30 of 30)

- [Misspecified Gaussian Process Bandit Optimization](https://mlsanity.com/paper/2111.05008/) (2021)
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- [Maximum Likelihood Estimation in Gaussian Process Regression is Ill-Posed](https://mlsanity.com/paper/2203.09179/) (2022)
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- [Robust and Conjugate Gaussian Process Regression](https://mlsanity.com/paper/2311.00463/) (2023)
- [Optimally-Weighted Estimators of the Maximum Mean Discrepancy for Likelihood-Free Inference](https://mlsanity.com/paper/2301.11674/) (2023)
- [Conditional Bayesian Quadrature](https://mlsanity.com/paper/2406.16530/) (2024)
- [Non-smooth Bayesian Optimization in Tuning Problems](https://mlsanity.com/paper/2109.07563/) (2021)
- [Data-Efficient Kernel Methods for Learning Differential Equations and Their Solution Operators: Algorithms and Error Analysis](https://mlsanity.com/paper/2503.01036/) (2025)
- [Measuring the robustness of Gaussian processes to kernel choice](https://mlsanity.com/paper/2106.06510/) (2021)
- [Introduction To Gaussian Process Regression In Bayesian Inverse Problems, With New ResultsOn Experimental Design For Weighted Error Measures](https://mlsanity.com/paper/2302.04518/) (2023)
- [Meta-Learning Hypothesis Spaces for Sequential Decision-making](https://mlsanity.com/paper/2202.00602/) (2022)
- [Nested Expectations with Kernel Quadrature](https://mlsanity.com/paper/2502.18284/) (2025)
- [Lifelong Bandit Optimization: No Prior and No Regret](https://mlsanity.com/paper/2210.15513/) (2022)
- [On Average-Case Error Bounds for Kernel-Based Bayesian Quadrature](https://mlsanity.com/paper/2202.10615/) (2022)
- [Bayesian Numerical Integration with Neural Networks](https://mlsanity.com/paper/2305.13248/) (2023)
- [Asymptotic Bounds for Smoothness Parameter Estimates in Gaussian Process Interpolation](https://mlsanity.com/paper/2203.05400/) (2022)
- [Gaussian Process Regression under Computational and Epistemic Misspecification](https://mlsanity.com/paper/2312.09225/) (2023)
- [Kernelized Normalizing Constant Estimation: Bridging Bayesian Quadrature and Bayesian Optimization](https://mlsanity.com/paper/2401.05716/) (2024)
- [Efficient optimization of expensive black-box simulators via marginal means, with application to neutrino detector design](https://mlsanity.com/paper/2508.01834/) (2025)
- [Bayesian Quadrature](https://mlsanity.com/paper/2602.16218/) (2026)
- [Antenna Array Calibration Via Gaussian Process Models](https://mlsanity.com/paper/2301.06582/) (2023)
- [Bandit Convex Optimisation Revisited: FTRL Achieves tildeO(t1/2) Regret](https://mlsanity.com/paper/2302.00358/) (2023)
- [PMBO: Enhancing Black-Box Optimization through Multivariate Polynomial Surrogates](https://mlsanity.com/paper/2403.07485/) (2024)
- [An interpretation of the Brownian bridge as a physics-informed prior for the Poisson equation](https://mlsanity.com/paper/2503.00213/) (2025)
- [Kernel Model Validation: How To Do It, And Why You Should Care](https://mlsanity.com/paper/2509.15244/) (2025)
- [BayesSum: Bayesian Quadrature in Discrete Spaces](https://mlsanity.com/paper/2512.16105/) (2025)
- [LAGO: A Local-Global Optimization Framework Combining Trust Region Methods and Bayesian Optimization](https://mlsanity.com/paper/2603.02970/) (2026)
- [Predictively Oriented Gaussian Process Posteriors](https://mlsanity.com/paper/2610.03201/) (2026)

## Abstract (arXiv)

Gaussian processes are ubiquitous in machine learning, statistics, and applied mathematics. They provide a flexible modelling framework for approximating functions, whilst simultaneously quantifying uncertainty. However, this is only true when the model is well-specified, which is often not the case in practice. In this paper, we study the properties of Gaussian process means when the smoothness of the model and the likelihood function are misspecified. In this setting, an important theoretical question of practial relevance is how accurate the Gaussian process approximations will be given the difficulty of the problem, our model and the extent of the misspecification. The answer to this problem is particularly useful since it can inform our choice of model and experimental design. In particular, we describe how the experimental design and choice of kernel and kernel hyperparameters can be adapted to alleviate model misspecification.