Geometric Inference for General High-Dimensional Linear Inverse Problems

Tony Cai
Department of Statistics
The Wharton School
University of Pennsylvania

In this talk, we present a unified theoretical framework for the analysis of a general ill-posed linear inverse model which includes as special cases noisy compressed sensing, sign vector recovery, trace regression, orthogonal matrix estimation, and noisy matrix completion. We propose computationally feasible convex programs and develop a theoretical framework to characterize the local rate of convergence for estimation accuracy, and to provide statistical inference procedures including confidence interval and hypothesis testing for parameters. The unified theory is built based on the local conic geometry and duality.