# Fast Gaussian Process Approximations for Autocorrelated Data

arXiv: https://arxiv.org/abs/2512.02925 · HTML: https://mlsanity.com/paper/2512.02925/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 11 of its 21 references that are in the map.
- First posted on arXiv 2 Dec 2025.

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

- [Distributed Gaussian Processes](https://mlsanity.com/paper/1502.02843/) (2015)
- [Local Gaussian process approximation for large computer experiments](https://mlsanity.com/paper/1303.0383/) (2013)
- [A Case Study Competition Among Methods for Analyzing Large Spatial Data](https://mlsanity.com/paper/1710.05013/) (2017)
- [Sparse Cholesky factorization by Kullback-Leibler minimization](https://mlsanity.com/paper/2004.14455/) (2020)
- [Vecchia approximations of Gaussian-process predictions](https://mlsanity.com/paper/1805.03309/) (2018)
- [Hierarchical Mixture-of-Experts Model for Large-Scale Gaussian Process Regression](https://mlsanity.com/paper/1412.3078/) (2014)
- [Scaled Vecchia approximation for fast computer-model emulation](https://mlsanity.com/paper/2005.00386/) (2020)
- [Correlation-based sparse inverse Cholesky factorization for fast Gaussian-process inference](https://mlsanity.com/paper/2112.14591/) (2021)
- [Cross-Validation for Correlated Data](https://mlsanity.com/paper/1904.02438/) (2019)
- [The temporal overfitting problem with applications in wind power curve modeling](https://mlsanity.com/paper/2012.01349/) (2020)
- [A Global-Local Approximation Framework for Large-Scale Gaussian Process Modeling](https://mlsanity.com/paper/2305.10158/) (2023)

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

- [Spatio-Temporal Gaussian Process for Building Terrain-Incorporating Wind Power Curves](https://mlsanity.com/paper/2607.00051/) (2026)
- [Domain-Adapted Power Curve for Cross-Farm Applications](https://mlsanity.com/paper/2607.19744/) (2026)

## Abstract (arXiv)

This paper is concerned with the problem of how to speed up computation for Gaussian process models trained on autocorrelated data. The Gaussian process model is a powerful tool commonly used in nonlinear regression applications. Standard regression modeling assumes random samples and an independently, identically distributed noise. Various fast approximations that speed up Gaussian process regression work under this standard setting. But for autocorrelated data, failing to account for autocorrelation leads to a phenomenon known as temporal overfitting that deteriorates model performance on new test instances. To handle autocorrelated data, existing fast Gaussian process approximations have to be modified; one such approach is to segment the originally correlated data points into blocks in which the blocked data are de-correlated. This work explains how to make some of the existing Gaussian process approximations work with blocked data. Numerical experiments across diverse application datasets demonstrate that the proposed approaches can remarkably accelerate computation for Gaussian process regression on autocorrelated data without compromising model prediction performance.