关于举行新加坡南洋理工大学潘光明教授学术报告的通知

报告题目：A Universal High-Dimensional Data Structural Detection Approach via the Largest Eigenvalue
报 告 人：潘光明  教授  (新加坡南洋理工大学)
报告时间：2016年7月5日（星期二）上午09:30-10:30
报告地点：4号楼4318室

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                                                                      数学学院
                                                                   2016年07月01日
报告摘要：
  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.