Work

Covariance operator estimation: Sparsity, lengthscale, and ensemble Kalman filters

Year: 2025

Type: article

Abstract: This paper investigates covariance operator estimation via thresholding. For Gaussian random fields with approximately sparse covariance operators, we establish non-asymptotic bounds on the estimation error in terms of the sparsity level of the covariance and the expected supremum of the field. We prove that thresholded estimators enjoy an exponential improvement in sample complexity compared with the standard sample covariance estimator if the field has a small correlation lengthscale. As an application of the theory, we study thresholded estimation of covariance operators within ensemble Kalman filters.

Source: Bernoulli

DOI: 10.3150/24-bej1809

Authors: Omar Al-Ghattas, Jiaheng Chen, Daniel Sanz-Alonso, Nathan Waniorek

Institution: University of Chicago

Language: English

Topic: Statistical Methods and Inference

Subfield: Statistics and Probability

Field: Mathematics

Domain: Physical Sciences

Open Access status: bronze

Funders: National Science Foundation, U.S. Department of Energy, Fundación BBVA, Banco Bilbao Vizcaya Argentaria

Awards: CAREER: Ensemble Kalman Methods and Bayesian Optimization in Inverse Problems and Data Assimilation, MACHINE-LEARNING ACCELERATED SIMULATIONS FOR FORECASTING, DATA ASSIMILATION, AND EXTREME EVENTS