# Gaussian Process Regression under Computational and Epistemic Misspecification

arXiv: https://arxiv.org/abs/2312.09225 · HTML: https://mlsanity.com/paper/2312.09225/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 12 of its 66 references that are in the map.
- First posted on arXiv 14 Dec 2023.

## Builds on (most cited first, 12 of 12)

- [Gaussian Processes and Kernel Methods: A Review on Connections and Equivalences](https://mlsanity.com/paper/1807.02582/) (2018)
- [Probabilistic Numerics and Uncertainty in Computations](https://mlsanity.com/paper/1506.01326/) (2015)
- [Convergence Guarantees for Gaussian Process Means With Misspecified Likelihoods and Smoothness](https://mlsanity.com/paper/2001.10818/) (2020)
- [Error Bounds for Learning with Vector-Valued Random Features](https://mlsanity.com/paper/2305.17170/) (2023)
- [Large Data and Zero Noise Limits of Graph-Based Semi-Supervised Learning Algorithms](https://mlsanity.com/paper/1805.09450/) (2018)
- [Generalization Bounds for Sparse Random Feature Expansions](https://mlsanity.com/paper/2103.03191/) (2021)
- [Operator-Valued Bochner Theorem, Fourier Feature Maps for Operator-Valued Kernels, and Vector-Valued Learning](https://mlsanity.com/paper/1608.05639/) (2016)
- [The SPDE approach for Gaussian and non-Gaussian fields: 10 years and still running](https://mlsanity.com/paper/2111.01084/) (2021)
- [Scalable Gaussian Process Computations Using Hierarchical Matrices](https://mlsanity.com/paper/1808.03215/) (2018)
- [The rational SPDE approach for Gaussian random fields with general smoothness](https://mlsanity.com/paper/1711.04333/) (2017)
- [Regularity and convergence analysis in Sobolev and H"older spaces for generalized Whittle-Mat'ern fields](https://mlsanity.com/paper/1904.06569/) (2019)
- [Graph-based Prior and Forward Models for Inverse Problems on Manifolds with Boundaries](https://mlsanity.com/paper/2106.06787/) (2021)

## Built on by (most cited first, 2 of 2)

- [Depth-Constrained ASV Navigation with Deep RL and Limited Sensing](https://mlsanity.com/paper/2504.18253/) (2025)
- [Bayesian Optimization on Networks](https://mlsanity.com/paper/2510.27643/) (2025)

## Abstract (arXiv)

Gaussian process regression is a classical kernel method for function estimation and data interpolation. In large data applications, computational costs can be reduced using low-rank or sparse approximations of the kernel. This paper investigates the effect of such kernel approximations on the interpolation error. We introduce a unified framework to analyze Gaussian process regression under important classes of computational misspecification: Karhunen-Lo`eve expansions that result in low-rank kernel approximations, multiscale wavelet expansions that induce sparsity in the covariance matrix, and finite element representations that induce sparsity in the precision matrix. Our theory also accounts for epistemic misspecification in the choice of kernel parameters.