We study the problem of recovery of matrices that are simultaneously low rank and row
and/or column sparse. Such matrices appear in recent applications in cognitive …

Many optimization problems over matrices arising in applications are believed to have low-
rank solutions. We may be able to efficiently solve such problems by optimizing only over …

Existing results for low-rank matrix recovery largely focus on quadratic loss, which enjoys
favorable properties such as restricted strong convexity/smoothness (RSC/RSM) and well …

This thesis considers estimation and statistical inference for high dimensional model with
constrained parameter space. Due to the recent development of data storage and computing …

For high-dimensional data, two of the most important questions are the question of
algorithmic optimality, which asks for the optimal algorithm within a certain class of …

In recent years, extensive research has focused on the $\ell_1 $ penalized least squares
(Lasso) estimators of high-dimensional regression when the number of covariates $ p $ is …