Scalable Model-Based Gaussian Process Clustering

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 $O(p^2)$ space complexity and $O(p^3)$ 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 (\href{https://www.ncei.noaa.gov/access/monitoring/climate-at-a-glance/global/time-series}{noaa.gov}) data-sets.