Online Change-Point Detection of Linear Regression Models

Abstract

In this paper, we consider the problem of quickly detecting an abrupt change in linear regression models. Specifically, an observer sequentially obtains a sequence of observations, whose underlying linear model changes at an unknown time. Moreover, the pre-change linear model is perfectly known by the observer but the post-change linear model is unknown. The observer aims to design an efficient online algorithm to detect the presence of the change via his sequential observations. Based on different assumptions on the change-point, both non-Bayesian and Bayesian problem formulations are considered. In the non-Bayesian setting, the change-point is modeled as a fixed but unknown constant. Two performance metrics, namely the worst case detection delay and the average run length to false alarm, are adopted to evaluate the performance of detection algorithms. In the Bayesian setting, the change-point is modeled as a geometrically distributed random variable. For this case, the average detection delay and the probability of false alarm are used as performance metrics. We propose a novel algorithm, namely the parallel-sum algorithm, for the purpose of change detection. For both setups, we show that the proposed algorithm has a low computational complexity while still offering a good performance in terms of the performance metrics of the respective setting.