A Markov random field model for change points detection

Abstract

Detecting Change Points (CPs) in data sequences is a challenging problem that arises in a variety of disciplines, including signal processing and time series analysis. While many methods exist for PieceWise Constant (PWC) signals, relatively fewer address PieceWise Linear (PWL) signals due to the challenge of preserving sharp transitions. This paper introduces a Markov Random Field (MRF) model for detecting changes in slope. The number of CPs and their locations are unknown. The proposed method incorporates PWL prior information using MRF framework with an additional boolean variable called Line Process (LP), describing the presence or absence of CPs. The solution is then estimated in the sense of maximum a posteriori. The LP allows us to define a non-convex non-smooth energy function that is algorithmically hard to minimize. To tackle the optimization challenge, we propose an extension of the combinatorial algorithm DPS, initially designed for CP detection in PWC signals. Also, we present a shared memory implementation to enhance computational efficiency. Numerical studies show that the proposed model produces competitive results compared to the state-of-the-art methods. We further evaluate the performance of our method on three real datasets, demonstrating superior and accurate estimates of the underlying trend compared to competing methods.