5 papers · 1 filter
Convergence Rates for Learning Pseudo-Differential Operators
Jiaheng Chen, Daniel Sanz-Alonso
This paper establishes convergence rates for learning elliptic pseudo-differential operators, a fundamental operator class in partial differential equations and mathematical physic…
On the Estimation of Gaussian Moment Tensors
Omar Al-Ghattas, Jiaheng Chen, Daniel Sanz-Alonso
This paper studies two estimators for Gaussian moment tensors: the standard sample moment estimator and a plug-in estimator based on Isserlis's theorem. We establish dimension-free…
Precision and Cholesky Factor Estimation for Gaussian Processes
Jiaheng Chen, Daniel Sanz-Alonso
This paper studies the estimation of large precision matrices and Cholesky factors obtained by observing a Gaussian process at many locations. Under general assumptions on the prec…
Optimal Estimation of Structured Covariance Operators
Omar Al-Ghattas, Jiaheng Chen, Daniel Sanz-Alonso +1
This paper establishes optimal convergence rates for estimation of structured covariance operators of Gaussian processes. We study banded operators with kernels that decay rapidly…
Covariance Operator Estimation: Sparsity, Lengthscale, and Ensemble Kalman Filters
Omar Al-Ghattas, Jiaheng Chen, Daniel Sanz-Alonso +1
This paper investigates covariance operator estimation via thresholding. For Gaussian random fields with approximately sparse covariance operators, we establish non-asymptotic boun…