# Scalable Model-Based Gaussian Process Clustering

arXiv: https://arxiv.org/abs/2309.07882 · HTML: https://mlsanity.com/paper/2309.07882/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 9 of its 26 references that are in the map.
- First posted on arXiv 14 Sep 2023.

## Builds on (most cited first, 9 of 9)

- [Hierarchical Nearest-Neighbor Gaussian Process Models for Large Geostatistical Datasets](https://mlsanity.com/paper/1406.7343/) (2014)
- [A general framework for Vecchia approximations of Gaussian processes](https://mlsanity.com/paper/1708.06302/) (2017)
- [Sparse Cholesky factorization by Kullback-Leibler minimization](https://mlsanity.com/paper/2004.14455/) (2020)
- [Permutation and Grouping Methods for Sharpening Gaussian Process Approximations](https://mlsanity.com/paper/1609.05372/) (2016)
- [Vecchia approximations of Gaussian-process predictions](https://mlsanity.com/paper/1805.03309/) (2018)
- [Scaled Vecchia approximation for fast computer-model emulation](https://mlsanity.com/paper/2005.00386/) (2020)
- [Scalable Bayesian Optimization Using Vecchia Approximations of Gaussian Processes](https://mlsanity.com/paper/2203.01459/) (2022)
- [Hierarchical sparse Cholesky decomposition with applications to high-dimensional spatio-temporal filtering](https://mlsanity.com/paper/2006.16901/) (2020)
- [Detecting British Columbia Coastal Rainfall Patterns by Clustering Gaussian Processes](https://mlsanity.com/paper/1812.09758/) (2018)

## Built on by (most cited first, 1 of 1)

- [Distance-Aware Error for Spline Networks: A Bottom-Up Approach to Uncertainty](https://mlsanity.com/paper/2501.04757/) (2025)

## Abstract (arXiv)

Gaussian process is an indispensable tool in clustering functional data, owing to it's flexibility and inherent uncertainty quantification. However, when the functional data is observed over a large grid (say, of length p), Gaussian process clustering quickly renders itself infeasible, incurring O(p2) space complexity and O(p3) time complexity per iteration; and thus prohibiting it's natural adaptation to large environmental applications. To ensure scalability of Gaussian process clustering in such applications, we propose to embed the popular Vecchia approximation for Gaussian processes at the heart of the clustering task, provide crucial theoretical insights towards algorithmic design, and finally develop a computationally efficient expectation maximization (EM) algorithm. Empirical evidence of the utility of our proposal is provided via simulations and analysis of polar temperature anomaly (hrefhttps://www.ncei.noaa.gov/access/monitoring/climate-at-a-glance/global/time-seriesnoaa.gov) data-sets.