Integrating multiple random sketches for sufficient dimension reduction in large-p-small-n problems

Abstract

Sufficient dimension reduction (SDR) is continuing an active research field nowadays. When estimating the central subspace (CS), inverse regression based SDR methods involve solving a generalized eigenvalue problem, which can be problematic under the large-p-small-n situation. In recent years, there are emerging new techniques in numerical linear algebra, called randomized algorithms or random sketching, for high dimensional and large scale problems. To overcome the large-p-small-n problem in SDR, we combine the idea of statistical inference with random sketching to propose a new SDR method, named integrated random-partition SDR (iRP-SDR). Our method consists of the following steps. (1) Randomly partition the covariates into subsets to construct an envelope subspace with low dimension. (2) Obtain a sketch estimate of the CS by applying conventional SDR method in the constructed envelope subspace. (3) Repeat the above two steps for multiple times and integrate these multiple sketches to form a final estimate of the CS. The advantageous performance of iRP-SDR is demonstrated via simulation studies and an EEG data analysis. (joint with Hung Hung, National Taiwan University)線上參與辦法請見:https://webconf.vc.dfn.de/optimization（Virtual seminar room: webconf.vc.dfn.de/optimization Room Passcode:? seed）SEED活動資訊請見以下頁面:https://seed.stat.nus.edu.sg/index.php/events