A SHRINKAGE PRINCIPLE FOR HEAVY-TAILED DATA: HIGH-DIMENSIONAL ROBUST LOW-RANK MATRIX RECOVERY.

ABSTRACT: This paper introduces a simple principle for robust statistical inference via appropriate shrinkage on the data. This widens the scope of high-dimensional techniques, reducing the distributional conditions from sub-exponential or sub-Gaussian to more relaxed bounded second or fourth moment. As an illustration of this principle, we focus on robust estimation of the low-rank matrix Θ* from the trace regression model Y = Tr(Θ*^⊤ X) + ϵ. It encompasses four popular problems: sparse linear model, compressed sensing, matrix completion and multi-task learning. We propose to apply the penalized least-squares approach to the appropriately truncated or shrunk data. Under only bounded 2+δ moment condition on the response, the proposed robust methodo

SUBMITTER: Fan J 

PROVIDER: S-EPMC8457508 | biostudies-literature | 2021 Jun

REPOSITORIES: biostudies-literature