Dear Colleagues, The ASA Statistical Learning and Data Science Section is pleased to announce the September webinar, presented by Dr. Hui Zou on September 27, 2022.
Title: Sparse Convoluted Rank Regression in High Dimensions
Speakers: Dr. Hui Zou, School of Statistics, University of Minnesota, Twin Cities
Date and Time: September 27, 2022, 2:00 to 3:30 pm Eastern Time
Registration Link: ASA SLDS Webinar Registration Link [eventbrite.com]
Abstract: Wang et al. (2020, JASA) studied the high-dimensional sparse penalized rank regression and established its nice theoretical properties. However, the computation of penalized rank regression can be very challenging for high-dimensional data, due to the highly nonsmooth rank regression loss. In this work we view the rank regression loss as a non-smooth empirical counterpart of a population level quantity, and a smooth empirical counterpart is derived by substituting a kernel density estimator for the true distribution in the expectation calculation. This view leads to the convoluted rank regression loss and consequently the sparse penalized convoluted rank regression (CRR) for high-dimensional data. Under the same key assumptions for sparse rank regression, we establish the rate of convergence of the $\ell_1$-penalized CRR for a tuning free penalization parameter and prove the strong oracle property of the folded concave penalized CRR. We further propose a high-dimensional Bayesian information criterion for selecting the penalization parameter in folded concave penalized CRR and prove its selection consistency. We derive an efficient algorithm for solving sparse convoluted rank regression that scales well with high dimensions. Numerical examples demonstrate the promising performance of the sparse convoluted rank regression over the sparse rank regression. Our theoretical and numerical results suggest that sparse convoluted rank regression enjoys the best of both sparse least squares regression and sparse rank regression. Presenter: Hui Zou received PhD in Statistics from Stanford University in 2005 and became a full professor of Statistics at University of Minnesota in 2014. His research interests include high-dimensional statistics, machine learning, and data science in general. He is an elected Fellow of Institute of Mathematical Statistics and American Statistical Association. He has been Web of Science highly cited researcher in mathematics from 2014 to 2019.