Invited Speaker Series

Fall 2022

 A structured covariance ensemble for sufficient dimension reduction

Dr. Yuan Xue, Associate Professor | University of International Business and Economics

Date: November 4, 2022, 8:30-9:30am, virtual via Zoom

Abstract:Sufficient dimension reduction (SDR) is a useful tool for high-dimensional data analysis. SDR aims at reducing the data dimensionality without loss of regression information between the response and its high-dimensional predictors. Many existing SDR methods are designed for the data with continuous responses. Motivated by a recent work on aggregate dimension reduction, we propose a unified SDR framework for both continuous and binary responses through a structured covariance ensemble. The connection with existing approaches is discussed in details and an efficient algorithm is proposed. Numerical examples and a real data application demonstrate its satisfactory performance.

On projective resampling for sufficient dimension reduction with random response objects

Dr. Abdul-Nasah SoalseUniversity of Notre Dame

Date: October 22, 2022, 8:30-9:30am, virtual via Zoom

Abstract: Technological advancement has led to the collection of novel data with response objects which may not lie in the Euclidean space. Typical scenarios include cases where the response objects are probability distributions, covariance matrices, graph Laplacians, or spheres. A sufficient dimension reduction (SDR) method to solve these types of problems using a projective resampling technique is proposed. The complex response objects are first mapped to a real-valued distance matrix using the appropriate metric, which is then projected onto a unit vector on a hypersphere to obtain univariate Euclidean-valued response. Based on the projected response, the corresponding dimension reduction subspace in the direction of the unit vector is estimated using classical SDR methods such as ordinary least squares, sliced inverse regression, and sliced average variance estimation. Several vectors on the unit hypersphere are sampled and their subspaces averaged to estimate the central subspace. The projection technique avoids the curse of dimensionality associated with generating high dimensional kernels and relies on fewer tuning parameters while preserving the joint distribution of the response object. An extensive simulation study demonstrates the performance of our proposal on synthetic data. The analysis of the distribution of county-level COVID-19 spread in the United States as a function of socio-economic and demographic characteristics is also provided. The theoretical justifications are included as well.

Spring 2023