32 citations · 183 across the 54 of their papers we have counts for
11 papers · 1 filter
Non-asymptotic Analysis of Matérn Regression: The Roles of Target and Kernel Lengthscales
Daniel Sanz-Alonso
Theoretical guarantees for kernel regression are typically formulated in terms of smoothness, but practical accuracy depends critically on how the design resolution compares with t…
Optimal Multiscale Learning of Linear Operators
Jiaheng Chen, Daniel Sanz-Alonso
We study the statistical and computational limits of learning bounded linear operators between Sobolev spaces from noisy input-output data. In wavelet coordinates, the problem is r…
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 via Adaptive Thresholding
Omar Al-Ghattas, Daniel Sanz-Alonso
This paper studies sparse covariance operator estimation for nonstationary processes with sharply varying marginal variance and small correlation lengthscale. We introduce a covari…
Hierarchical Bayesian Inverse Problems: A High-Dimensional Statistics Viewpoint
Daniel Sanz-Alonso, Nathan Waniorek
This paper analyzes hierarchical Bayesian inverse problems using techniques from high-dimensional statistics. Our analysis leverages a property of hierarchical Bayesian regularizer…
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…
Unlabeled Data Help in Graph-Based Semi-Supervised Learning: A Bayesian Nonparametrics Perspective
Daniel Sanz-Alonso, Ruiyi Yang
In this paper we analyze the graph-based approach to semi-supervised learning under a manifold assumption. We adopt a Bayesian perspective and demonstrate that, for a suitable choi…
The Bayesian update: variational formulations and gradient flows
Nicolas Garcia Trillos, Daniel Sanz-Alonso
The Bayesian update can be viewed as a variational problem by characterizing the posterior as the minimizer of a functional. The variational viewpoint is far from new and is at the…