Asymptotic Distribution-free Change-point Detection for Modern Data Based on a New Ranking Scheme

Abstract: Change-point detection (CPD) involves identifying distributional changes in a sequence of independent observations. Among nonparametric methods, rank-based methods are attractive due to their robustness and effectiveness and have been extensively studied for univariate data. However, they are not well explored for high-dimensional or non-Euclidean data. This paper proposes a new method, Rank INduced by Graph Change-Point Detection (RING-CPD), which utilizes graph-induced ranks to handle high-dimensional and non-Euclidean data. The new method is asymptotically distribution-free under the null hypothesis, and an analytic $p$-value approximation is provided for easy type-I error control. Simulation studies show that RING-CPD effectively detects change points across a wide range of alternatives and is also robust to heavy-tailed distribution and outliers. The new method is illustrated by the detection of seizures in a functional connectivity network dataset, changes of digit images, and travel pattern changes in the New York City Taxi dataset.