Abstract

Sufficient dimension reduction (SDR) is known to be a powerful tool for achieving data reduction and visualization in regression and classification problems. In this work, we study high dimensional SDR problems and propose solutions under a unified minimum discrepancy approach with regularization. When p grows exponentially fast with n, consistency results in both central subspace estimation and variable selection are established simultaneously for important SDR methods. The proposed approach is equipped with a new algorithm to efficiently solve regularized objective functions without the need to invert a large covariance matrix. We further study a unified framework of SDR to high-dimensional survival analysis under weak modeling assumptions. This framework includes many popular survival regression models as special cases, and produces a number of practically useful outputs with theoretical guarantees, including a uniformly consistent Kaplan-Meier type estimator of the conditional distribution function of the survival time and a consistent estimator of the conditional quantile survival time in high dimension. Promising applications of our proposal are demonstrated through simulations and real data analysis on biomedical studies.

For more information about Shanshan visit: https://sites.google.com/a/udel.edu/sding/home

Watch Stream