Stat Colloquium [Virtual]: Dr. Qing Mai

Title: Robust Sliced Inverse Regression: Optimal Estimation for Heavy-Tailed Data in High Dimensions

Abstract: Sliced inverse regression (SIR) is a flexible modeling tool that effectively reduces dimensions to reveal the complicated mechanism behind data. In recent years, SIR has been generalized to high dimensions in a variety of ways. However, all existing methods rely on the light-tailed assumption for predictors, which is frequently violated in real life. To tackle ubiquitous heavy-tailed data, we propose a novel robust SIR method, referred to as ROSE, that scales well with high dimensions and heavy tails simultaneously. We start with an adaptive distribution model that explicitly incorporates heavy tails and covers many popular distributions as special cases. Then ROSE leverages a new elegant invariance result to convert the original SIR problem to a less challenging one on a set of latent light-tailed predictors. We rigorously show that ROSE admits the same minimax optimal convergence rate as existing light-tailed methods even when we only have finite second moments. ROSE is also computationally efficient compared to existing robust methods in that no extra tuning parameter selection is required to overcome the heavy-tailedness. Extensive empirical studies are conducted to support the theoretical results.