A Sharp Analysis of Covariate Adjusted Precision Matrix Estimation via Alternating Gradient Descent with Hard Thresholding

In this paper, we present a sharp analysis for an alternating gradient descent algorithm which is used to solve the covariate adjusted precision matrix estimation problem in the high dimensional setting. Without the resampling assumption, we demonstrate that this algorithm not only enjoys a linear rate of convergence, but also attains the optimal statistical rate (i.e., minimax rate). Moreover, our analysis also characterizes the time-data tradeoffs in the covariate adjusted precision matrix estimation problem. Numerical experiments are provided to verify our theoretical results.