77 citations · 198 across the 22 of their papers we have counts for
5 papers · 1 filter
Uniform error bound for PCA matrix denoising
Xin T. Tong, Wanjie Wang, Yuguan Wang
Principal component analysis (PCA) is a simple and popular tool for processing high-dimensional data. We investigate its effectiveness for matrix denoising. We consider the clean d…
Consistency analysis of bilevel data-driven learning in inverse problems
Neil K. Chada, Claudia Schillings, Xin T. Tong +1
One fundamental problem when solving inverse problems is how to find regularization parameters. This article considers solving this problem using data-driven bilevel optimization,…
Spatial localization for nonlinear dynamical stochastic models for excitable media
Nan Chen, Andrew J. Majda, Xin T. Tong
Nonlinear dynamical stochastic models are ubiquitous in different areas. Excitable media models are typical examples with large state dimensions. Their statistical properties are o…
Rigorous Analysis for Efficient Statistically Accurate Algorithms for Solving Fokker-Planck Equations in Large Dimensions
Nan Chen, Andrew J. Majda, Xin T. Tong
This article presents a rigorous analysis for efficient statistically accurate algorithms for solving the Fokker-Planck equations associated with high-dimensional nonlinear turbule…
Rigorous accuracy and robustness analysis for two-scale reduced random Kalman filters in high dimensions
Andrew J. Majda, Xin T. Tong
Contemporary data assimilation often involves millions of prediction variables. The classical Kalman filter is no longer computationally feasible in such a high dimensional context…