# Adaptive sparse variational approximations for Gaussian process regression

arXiv: https://arxiv.org/abs/2504.03321 · HTML: https://mlsanity.com/paper/2504.03321/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 12 of its 34 references that are in the map.
- First posted on arXiv 4 Apr 2025.

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

- [GPyTorch: Blackbox Matrix-Matrix Gaussian Process Inference with GPU Acceleration](https://mlsanity.com/paper/1809.11165/) (2018)
- [Gaussian Processes for Big Data](https://mlsanity.com/paper/1309.6835/) (2013)
- [Convergence of Sparse Variational Inference in Gaussian Processes Regression](https://mlsanity.com/paper/2008.00323/) (2020)
- [Convergence Rates of Variational Posterior Distributions](https://mlsanity.com/paper/1712.02519/) (2017)
- [Variational Bayes for high-dimensional linear regression with sparse priors](https://mlsanity.com/paper/1904.07150/) (2019)
- [Posterior and Computational Uncertainty in Gaussian Processes](https://mlsanity.com/paper/2205.15449/) (2022)
- [Consistency of Variational Bayes Inference for Estimation and Model Selection in Mixtures](https://mlsanity.com/paper/1805.05054/) (2018)
- [Adaptive variational Bayes: Optimality, computation and applications](https://mlsanity.com/paper/2109.03204/) (2021)
- [Bayesian Model Selection via Mean-Field Variational Approximation](https://mlsanity.com/paper/2312.10607/) (2023)
- [Convergence Rates of Empirical Bayes Posterior Distributions: A Variational Perspective](https://mlsanity.com/paper/2009.03969/) (2020)
- [Variational Gaussian Processes For Linear Inverse Problems](https://mlsanity.com/paper/2311.00663/) (2023)
- [Contraction rates for conjugate gradient and Lanczos approximate posteriors in Gaussian process regression](https://mlsanity.com/paper/2406.12678/) (2024)

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

- [Adaptive Resolution for Finite-Rank Gaussian Processes](https://mlsanity.com/paper/2505.24066/) (2025)
- [Fast rates in Bayesian online learning with approximate posteriors](https://mlsanity.com/paper/2608.25706/) (2026)

## Abstract (arXiv)

Accurate tuning of hyperparameters is crucial to ensure that models can generalise effectively across different settings. In this paper, we present theoretical guarantees for hyperparameter selection using variational Bayes in the nonparametric regression model. We construct a variational approximation to a hierarchical Bayes procedure, and derive upper bounds for the contraction rate of the variational posterior in an abstract setting. The theory is applied to various Gaussian process priors and variational classes, resulting in minimax optimal rates. Our theoretical results are accompanied with numerical analysis both on synthetic and real world data sets.