报告人：Richard Samworth 教授
主题： High-dimensional Changepoint Estimation via Sparse Projection
内容简介： Changepoints are a very common feature of Big Data that arrive in the form of a data stream. 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 changepoints: first, we argue that a good projection direction can be obtained as the leading left singular vector of the matrix that solves a convex optimization problem derived from the CUSUM transformation of the time series. We then apply an existing univariate changepoint estimation algorithm to the projected series. Our theory provides strong guarantees on both the number of estimated changepoints 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’.
Professor of Statistics in the Statistical Laboratory from the Faculty of Mathematics at the University of Cambridge.