# Correlation-based sparse inverse Cholesky factorization for fast Gaussian-process inference

arXiv: https://arxiv.org/abs/2112.14591 · HTML: https://mlsanity.com/paper/2112.14591/

## Key facts

- Cited by 12 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 29 Dec 2021.

## Built on by (most cited first, 12 of 12)

- [Scalable Bayesian Optimization Using Vecchia Approximations of Gaussian Processes](https://mlsanity.com/paper/2203.01459/) (2022)
- [Variational Nearest Neighbor Gaussian Process](https://mlsanity.com/paper/2202.01694/) (2022)
- [Variational sparse inverse Cholesky approximation for latent Gaussian processes via double Kullback-Leibler minimization](https://mlsanity.com/paper/2301.13303/) (2023)
- [Vecchia Gaussian Process Ensembles on Internal Representations of Deep Neural Networks](https://mlsanity.com/paper/2305.17063/) (2023)
- [Neighbour-Driven Gaussian Process Variational Autoencoders for Scalable Structured Latent Modelling](https://mlsanity.com/paper/2505.16481/) (2025)
- [A Spatio-Temporal Machine Learning Model for Mortgage Credit Risk: Default Probabilities and Loan Portfolios](https://mlsanity.com/paper/2410.02846/) (2024)
- [Fast Gaussian Process Approximations for Autocorrelated Data](https://mlsanity.com/paper/2512.02925/) (2025)
- [Adaptive LASSO estimation for functional hidden dynamic geostatistical model](https://mlsanity.com/paper/2208.05528/) (2022)
- [Learning non-Gaussian spatial distributions via Bayesian transport maps with parametric shrinkage](https://mlsanity.com/paper/2409.19208/) (2024)
- [Vecchia-Inducing-Points Full-Scale Approximations for Gaussian Processes](https://mlsanity.com/paper/2507.05064/) (2025)
- [A Streaming Sparse Cholesky Method for Derivative-Informed Gaussian Process Surrogates Within Digital Twin Applications](https://mlsanity.com/paper/2511.00366/) (2025)
- [Scalable Derivative Gaussian Processes via Exact Gradient Reduction](https://mlsanity.com/paper/2606.02909/) (2026)

## Abstract (arXiv)

Gaussian processes are widely used as priors for unknown functions in statistics and machine learning. To achieve computationally feasible inference for large datasets, a popular approach is the Vecchia approximation, which is an ordered conditional approximation of the data vector that implies a sparse Cholesky factor of the precision matrix. The ordering and sparsity pattern are typically determined based on Euclidean distance of the inputs or locations corresponding to the data points. Here, we propose instead to use a correlation-based distance metric, which implicitly applies the Vecchia approximation in a suitable transformed input space. The correlation-based algorithm can be carried out in quasilinear time in the size of the dataset, and so it can be applied even for iterative inference on unknown parameters in the correlation structure. The correlation-based approach has two advantages for complex settings: It can result in more accurate approximations, and it offers a simple, automatic strategy that can be applied to any covariance, even when Euclidean distance is not applicable. We demonstrate these advantages in several settings, including anisotropic, nonstationary, multivariate, and spatio-temporal processes. We also illustrate our method on multivariate spatio-temporal temperature fields produced by a regional climate model.