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Activity Number: 449 - Recent Advances in Change-Point Detection and Segmentation
Type: Invited
Date/Time: Wednesday, August 1, 2018 : 8:30 AM to 10:20 AM
Sponsor: Section on Nonparametric Statistics
Abstract #325460 Presentation
Title: High-Dimensional Change Point Estimation via Sparse Projection
Author(s): Tengyao Wang* and Richard J Samworth
Companies: University of Cambridge and University of Cambridge
Keywords: change point estimation; segmentation; piecewise stationary; sparsity; convex optimisation; dimension reduction

Change points are a very common feature of Big Data that arrive in the form of a data stream. In this paper, we study high-dimensional time series in which, at certain time points, the mean structure changes in a sparse subset of the coordinates. The challenge is to borrow strength across the coordinates in order to detect smaller changes than could be observed in any individual component series. We propose a two-stage procedure called 'inspect' for estimation of the change points: first, we argue that a good projection direction can be obtained as the leading left singular vector of the matrix that solves a convex optimisation problem derived from the CUSUM transformation of the time series. We then apply an existing univariate change point estimation algorithm to the projected series. Our theory provides strong guarantees on both the number of estimated change points and the rates of convergence of their locations, and our numerical studies validate its highly competitive empirical performance for a wide range of data generating mechanisms. Software implementing the methodology is available in the R package 'InspectChangepoint'.

Authors who are presenting talks have a * after their name.

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