High-dimensional changepoint estimation via sparse projection

TL;DR

This paper introduces a novel two-stage method called 'inspect' for detecting sparse mean shifts in high-dimensional time series data, combining convex optimization and univariate changepoint detection with strong theoretical guarantees.

Contribution

It proposes a new approach for high-dimensional changepoint detection that effectively leverages sparse projections and provides rigorous theoretical analysis.

Findings

Method achieves accurate changepoint detection in high-dimensional settings.

Theoretical guarantees on the number and location accuracy of estimated changepoints.

Validated performance across diverse data scenarios.

Abstract

Changepoints 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 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 optimisation 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'.