# Calibrated Computation-Aware Gaussian Processes

arXiv: https://arxiv.org/abs/2410.08796 · HTML: https://mlsanity.com/paper/2410.08796/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Builds on 7 of its 34 references that are in the map.
- First posted on arXiv 11 Oct 2024.

## Builds on (most cited first, 7 of 7)

- [Validating Bayesian Inference Algorithms with Simulation-Based Calibration](https://mlsanity.com/paper/1804.06788/) (2018)
- [Bayesian Probabilistic Numerical Methods](https://mlsanity.com/paper/1702.03673/) (2017)
- [Posterior and Computational Uncertainty in Gaussian Processes](https://mlsanity.com/paper/2205.15449/) (2022)
- [Preconditioning for Scalable Gaussian Process Hyperparameter Optimization](https://mlsanity.com/paper/2107.00243/) (2021)
- [Computation-Aware Kalman Filtering and Smoothing](https://mlsanity.com/paper/2405.08971/) (2024)
- [Probabilistic Linear Solvers for Machine Learning](https://mlsanity.com/paper/2010.09691/) (2020)
- [Probabilistic Iterative Methods for Linear Systems](https://mlsanity.com/paper/2012.12615/) (2020)

## Built on by (most cited first, 6 of 6)

- [Computation-Aware Gaussian Processes: Model Selection And Linear-Time Inference](https://mlsanity.com/paper/2411.01036/) (2024)
- [Online Conformal Probabilistic Numerics via Adaptive Edge-Cloud Offloading](https://mlsanity.com/paper/2503.14453/) (2025)
- [Randomised Postiterations for Calibrated BayesCG](https://mlsanity.com/paper/2504.04247/) (2025)
- [Robust and Computation-Aware Gaussian Processes](https://mlsanity.com/paper/2505.21133/) (2025)
- [Learning to Solve Related Linear Systems](https://mlsanity.com/paper/2503.17265/) (2025)
- [Affine Tracing: A New Paradigm for Probabilistic Linear Solvers](https://mlsanity.com/paper/2605.10566/) (2026)

## Abstract (arXiv)

Gaussian processes are notorious for scaling cubically with the size of the training set, preventing application to very large regression problems. Computation-aware Gaussian processes (CAGPs) tackle this scaling issue by exploiting probabilistic linear solvers to reduce complexity, widening the posterior with additional computational uncertainty due to reduced computation. However, the most commonly used CAGP framework results in (sometimes dramatically) conservative uncertainty quantification, making the posterior unrealistic in practice. In this work, we prove that if the utilised probabilistic linear solver is calibrated, in a rigorous statistical sense, then so too is the induced CAGP. We thus propose a new CAGP framework, CAGP-GS, based on using Gauss-Seidel iterations for the underlying probabilistic linear solver. CAGP-GS performs favourably compared to existing approaches when the test set is low-dimensional and few iterations are performed. We test the calibratedness on a synthetic problem, and compare the performance to existing approaches on a large-scale global temperature regression problem.