Divide and Conquer Dynamic Programming: An Almost Linear Time Change Point Detection Methodology in High Dimensions

TL;DR

This paper introduces Divide and Conquer Dynamic Programming (DCDP), a fast and versatile framework for detecting change points in high-dimensional time series data, achieving near-linear computational complexity and high accuracy.

Contribution

The paper presents a novel DCDP framework that is computationally efficient, broadly applicable, and provides theoretical guarantees for high-dimensional change point detection.

Findings

DCDP achieves almost linear computational complexity.

DCDP provides accurate change point estimates with sharp, often optimal, rates.

Extensive experiments validate DCDP's efficiency and accuracy on synthetic and real data.

Abstract

We develop a novel, general and computationally efficient framework, called Divide and Conquer Dynamic Programming (DCDP), for localizing change points in time series data with high-dimensional features. DCDP deploys a class of greedy algorithms that are applicable to a broad variety of high-dimensional statistical models and can enjoy almost linear computational complexity. We investigate the performance of DCDP in three commonly studied change point settings in high dimensions: the mean model, the Gaussian graphical model, and the linear regression model. In all three cases, we derive non-asymptotic bounds for the accuracy of the DCDP change point estimators. We demonstrate that the DCDP procedures consistently estimate the change points with sharp, and in some cases, optimal rates while incurring significantly smaller computational costs than the best available algorithms. Our findings are supported by extensive numerical experiments on both synthetic and real data.