  Change point detection in time series seeks to identify times 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 high-dimensional data: If any one variable changes, the whole
time series is assumed to have changed. However, in practical applications, we
may be interested only in certain components of the time series, exploring
abrupt changes in their distributions in the presence of other time series.
Here, assuming an underlying structural causal model that governs the
time-series data generation, we address this problem by proposing a two-stage
non-parametric algorithm that first learns parts of the causal structure
through constraint-based discovery methods. The algorithm then uses conditional
relative Pearson divergence estimation to identify the change points. The
conditional relative Pearson divergence quantifies the distribution disparity
between consecutive segments in the time series, while the causal discovery
method enables 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.
