Changepoint detection for high-dimensional time series with missing data

TL;DR

This paper introduces a new method for detecting change-points in high-dimensional time series data with missing elements by modeling data as lying near a low-dimensional, time-varying submanifold, improving detection robustness and efficiency.

Contribution

It presents a novel approach combining submanifold modeling, streaming data analysis, and recent high-dimensional techniques to effectively detect change-points with missing data.

Findings

Robust detection of abrupt changes in low-dimensional manifolds

Effective in high-dimensional settings with missing data

Outperforms classical methods in simulations and experiments

Abstract

This paper describes a novel approach to change-point detection when the observed high-dimensional data may have missing elements. The performance of classical methods for change-point detection typically scales poorly with the dimensionality of the data, so that a large number of observations are collected after the true change-point before it can be reliably detected. Furthermore, missing components in the observed data handicap conventional approaches. The proposed method addresses these challenges by modeling the dynamic distribution underlying the data as lying close to a time-varying low-dimensional submanifold embedded within the ambient observation space. Specifically, streaming data is used to track a submanifold approximation, measure deviations from this approximation, and calculate a series of statistics of the deviations for detecting when the underlying manifold has changed in a sharp or unexpected manner. The approach described in this paper leverages several recent results in the field of high-dimensional data analysis, including subspace tracking with missing data, multiscale analysis techniques for point clouds, online optimization, and change-point detection performance analysis. Simulations and experiments highlight the robustness and efficacy of the proposed approach in detecting an abrupt change in an otherwise slowly varying low-dimensional manifold.