Causal Discovery-Driven Change Point Detection in Time Series

Change point detection in time series aims to identify moments when the probability distribution of time series changes. It is widely applied in many areas, such as human activity sensing and medical science. In the context of multivariate time series, this typically involves examining the joint distribution of multiple variables: If the distribution of any one variable changes, the entire time series undergoes a distribution shift. However, in practical applications, we may be interested only in certain components of the time series, exploring abrupt changes in their distributions while accounting for the presence of other components. Here, assuming an underlying structural causal model that governs the time-series data generation, we address this task by proposing a two-stage non-parametric algorithm that first learns parts of the causal structure through constraint-based discovery methods, and then employs conditional relative Pearson divergence estimation to identify the change points. The conditional relative Pearson divergence quantifies the distribution difference between consecutive segments in the time series, while the causal discovery method allows a focus on the causal mechanism, facilitating access to independent and identically distributed (IID) samples. Theoretically, the typical assumption of samples being IID in conventional change point detection methods can be relaxed based on the Causal Markov Condition. Through experiments on both synthetic and real-world datasets, we validate the correctness and utility of our approach.