Change-point detection in variance-covariance matrix

TL;DR

This paper introduces a method for jointly estimating change points and the sparse covariance matrix in data that evolves in a piecewise constant manner, using penalized optimization and ADMM for efficiency.

Contribution

It proposes a novel approach combining Group Fused LASSO and LASSO with adaptive weights for accurate change point and covariance estimation, with theoretical consistency guarantees.

Findings

Method accurately detects change points in synthetic and real data.

Outperforms several competing procedures in experiments.

Efficient ADMM algorithm reduces computational complexity.

Abstract

We consider the joint estimation of change point locations and the sparsity pattern of the variance covariance matrix, which is assumed to evolve in a piecewise constant manner. By applying Group Fused LASSO and LASSO penalties to the squared Frobenius norm, we estimate both the covariance structure and the change points. Adaptive weights are incorporated into the penalty terms to enhance change point detection and covariance estimation accuracy. We establish the conditions under which the estimated change points and the sparse estimators within each segment are consistent. To solve the resulting optimization problem efficiently, we develop an alternating direction method of multipliers (ADMM) whose updates reduce to computationally tractable subproblems. The performance of the proposed method is illustrated through synthetic and real data experiments, including comparisons with several competing procedures.