# Adaptive Resolution for Finite-Rank Gaussian Processes

arXiv: https://arxiv.org/abs/2505.24066 · HTML: https://mlsanity.com/paper/2505.24066/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 11 of its 43 references that are in the map.
- First posted on arXiv 29 May 2025.

## Builds on (most cited first, 11 of 11)

- [Distributed Gaussian Processes](https://mlsanity.com/paper/1502.02843/) (2015)
- [Generalized Product of Experts for Automatic and Principled Fusion of Gaussian Process Predictions](https://mlsanity.com/paper/1410.7827/) (2014)
- [A Case Study Competition Among Methods for Analyzing Large Spatial Data](https://mlsanity.com/paper/1710.05013/) (2017)
- [Gaussian process emulators for computer experiments with inequality constraints](https://mlsanity.com/paper/1606.01265/) (2016)
- [Hierarchical Mixture-of-Experts Model for Large-Scale Gaussian Process Regression](https://mlsanity.com/paper/1412.3078/) (2014)
- [Adaptive distributed methods under communication constraints](https://mlsanity.com/paper/1804.00864/) (2018)
- [An asymptotic analysis of distributed nonparametric methods](https://mlsanity.com/paper/1711.03149/) (2017)
- [Deep Horseshoe Gaussian Processes](https://mlsanity.com/paper/2403.01737/) (2024)
- [Radial Neighbors for Provably Accurate Scalable Approximations of Gaussian Processes](https://mlsanity.com/paper/2211.14692/) (2022)
- [Efficient Bayesian shape-restricted function estimation with constrained Gaussian process priors](https://mlsanity.com/paper/1902.04701/) (2019)
- [Adaptive sparse variational approximations for Gaussian process regression](https://mlsanity.com/paper/2504.03321/) (2025)

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

- [Isotonic surrogate modeling for computer experiments with many input variables](https://mlsanity.com/paper/2609.35354/) (2026)
- [Finite-Rank Logistic Gaussian Processes with Exact Likelihood for Conditional Density Estimation](https://mlsanity.com/paper/2610.09452/) (2026)

## Abstract (arXiv)

Finite-rank approximations are widely used to scale Gaussian process (GP) regression, but their posterior behavior can differ from that of the corresponding parent GP prior. We study a class of finite-rank GP priors built from locally supported basis expansions with dependent Gaussian coefficients. Our framework covers finite-element approximations based on the stochastic partial differential equation (SPDE) representation of Mat'ern GPs and regular-grid GP interpolation schemes. We show that, with a suitable prior on the resolution parameter N, these finite-rank expansions inherit the same posterior contraction rate as the corresponding parent GP prior under the same bandwidth specification used for that parent prior. Consequently, the interpolation construction under a squared-exponential parent GP attains the minimax-optimal rate up to logarithmic factors under a hierarchical prior on the bandwidth parameter and on N, while the SPDE construction attains the same rate under a bandwidth scaling depending on the sample size and the smoothness of the true function, together with a prior on N. We also develop a posterior sampler for the hierarchical interpolation model that jointly updates the resolution and bandwidth parameters, and we provide numerical studies that support the theory.