Title:A Universal High-Dimensional Data Structural Detection Approach via the Largest Eigenvalue

Time: Tue, July 5, 2016, AM 09:30-10:30

Speaker:Prof. Pan Guangming (Nanyang technologgical University)

Location:Room 4318, Building No.4, Wushan Campus

Abstract:In this talk, we propose to deal with the high-dimensional change point detection problem from a new perspective–via the largest eigenvalue. The data dimension p diverges with the sample size n and can be larger than n. Without any specific parametric distribution assumptions and without any estimators, an optimization approach is proposed to figure out both the unknown number of change points and multiple change point positions simultaneously. What’s more, an adjustment term is introduced to handle sparse signals when the change only appears in few components out of the p dimension. The computation time is controlled at O(n^2) by adopting a dynamic programming, regardless of the true number of change points k0. Theoretical results are developed and various simulations are conducted to show the effectiveness of our method. Moreover, as applications, we discuss how to apply the idea proposed in this paper to some other high-dimensional data structure detection problems, e.g. equivalence testing of mean vectors and covariance matrices, which shows the universality of the proposed approach.