A0927
Title: Sparse Frechet sufficient dimension reduction with graphical structure among predictors
Authors: Jiaying Weng - Bentley University (United States) [presenting]
Abstract: Frechet regression has received considerable attention to model metric-space valued responses that are complex and non-Euclidean data, such as probability distributions and vectors on the unit sphere. However, existing Frechet regression literature focuses on the classical setting where the predictor dimension is fixed, and the sample size goes to infinity. The aim is to propose sparse Frechet sufficient dimension reduction with graphical structure among high-dimensional Euclidean predictors. In particular, a convex optimization problem is proposed that leverages the graphical information among predictors and avoids inverting the high-dimensional covariance matrix. The alternating direction method of multipliers (ADMM) algorithm is also provided to solve the optimization problem. Theoretically, the proposed method achieves subspace estimation and variable selection consistency under suitable conditions. Extensive simulations and real data analysis are carried out to illustrate the finite-sample performance of the proposed method.
