In this paper, we characterize sharp time-data tradeoffs for optimization problems used for
solving linear inverse problems. We focus on the minimization of a least-squares objective …

The generalized penalized constrained regression (G-PCR) is a penalized model for high-
dimensional linear inverse problems with structured features. This paper presents a sharp …

This manuscript studies a general approach to construct confidence sets for the solution of
population-level optimization, commonly referred to as M-estimation. Statistical inference for …

In this paper, we propose an abstract procedure for debiasing constrained or regularized
potentially high-dimensional linear models. It is elementary to show that the proposed …

In the past couple of decades, non-smooth convex optimization has emerged as a powerful
tool for the recovery of structured signals (sparse, low rank, etc.) from noisy linear or non …

Many important problems in contemporary machine learning involve solving highly
nonconvex problems in sampling, optimization, or games. The absence of convexity poses …

This paper presents a non-asymptotic upper bound for the estimation error of the
constrained lasso, under the high-dimensional (n≪ p) setting. In contrast to existing results …

Prior knowledge on properties of a target model often come as discrete or combinatorial
descriptions. This work provides a unified computational framework for defining norms that …

This paper presents an upper bound for the estimation error of the constrained lasso, under
the high-dimensional (n< p) setting. In contrast to existing results, the error bound in this …

In this thesis I consider three unconventional estimators and augment them with statistical
guarantees. First, I consider a cone projected power iteration algorithm designed to recover …