Random Interval Distillation for Detecting Multiple Changes in General Dependent Data

We propose a new and generic approach for detecting multiple change-points in general dependent data, termed random interval distillation (RID). By collecting random intervals with sufficient strength of signals and reassembling them into a sequence of informative short intervals, our new approach captures the shifts in signal characteristics across diverse dependent data forms including locally stationary high-dimensional time series and dynamic networks with Markov formation. We further propose a range of secondary refinements tailored to various data types to enhance the localization precision. Notably, for univariate time series and low-rank autoregressive networks, our methods achieve the minimax optimality as their independent counterparts. For practical applications, we introduce a clustering-based and data-driven procedure to determine the optimal threshold for signal strength, which is adaptable to a wide array of dependent data scenarios utilizing the connection between RID and clustering. Additionally, our method has been extended to identify kinks and changes in signals characterized by piecewise polynomial trends. We examine the effectiveness and usefulness of our methodology via extensive simulation studies and a real data example, implementing it in the R-package rid.