Statistics Colloquium Series

Date: 

Monday, October 24, 2022, 12:00pm to 1:00pm

Location: 

Science Center, Room 316

Our upcoming event for the Statistics Department Colloquium Series is scheduled for this Monday, October 24th from 12:00 – 1:00pm (ET) and will be an in-person presentation Science Center Rm. 316. The speaker will be Arian Maleki who is an Associate Professor in the Department of Statistics at Columbia University.

Title: Signal-to-noise-ratio aware minimaxity via higher order asymptotics

Abstract: The minimax framework is one of the most popular approaches for comparing the performance of different estimators and obtaining the optimal ones. Despite its popularity, the minimax framework suffers from a well-known issue: it focuses on the parts of the parameter space that are the most challenging for an estimation problem. For this reason, in many examples, the conclusions obtained from this framework can be misleading if translated and used in practice. To clarify this claim, we focus on the popular and well-studied example of the sparse Gaussian sequence model, and discuss the limitations of the existing results. We then propose a much more informative minimax framework that alleviates the major drawbacks of the classical one by controlling and monitoring the signal-to-noise-ratio (SNR) and sparsity level. Since the new SNR-aware minimx problems are more challenging to solve than the classical ones, we propose the higher-order asymptotic analysis that obtains accurate approximations of the minimax risk. Our framework alleviates some of the most pressing issues of the existing minimax results, and provides meaningful proposals for practitioners. Research done with Yilin Guo (Columbia University), Haolei Weng (Michigan State University), Arian Maleki (Columbia University).