ScanB-statistic for kernel change-point detection

Abstract

Detecting the emergence of an abrupt change-point is a classic problem in statistics and machine learning. Kernel-based nonparametric statistics have been used for this task, which enjoys fewer assumptions on the distributions than the parametric approach and can handle high-dimensional data. In this paper, we focus on the scenario when the amount of background data is large, and propose a computationally efficient kernel-based statistics for change-point detection, which are inspired by the recently developed B-statistics. A novel theoretical result of the paper is the characterization of the tail probability of these statistics using the change-of-measure technique, which focuses on characterizing the tail of the detection statistics rather than obtaining its asymptotic distribution under the null distribution. Such approximations are crucial to controlling the false alarm rate, which corresponds to the average-run-length in online change-point detection. Our approximations are shown to be highly accurate. Thus, they provide a convenient way to find detection thresholds for online cases without the need to resort to the more expensive simulations. We show that our methods perform well on both synthetic data and real data.

Change-Point Methods on a Sequence of Graphs

“…We note that the mean ARI is always close to zero, and it is significantly different from zero only in two settings. Overall, we conclude that E-div method was able to identify most of the change points, even in the most challenging sequence, Del 12,14,16,18,20 , which contains small changes in the distribution. Seizure detection: Here, we show results obtained on the Kaggle seizure detection problem, considering all available subjects.…”

Optimal Transport Based Change Point Detection and Time Series Segment Clustering

“…The nominal approach in the offline case would be to label local maxima above some threshold parameter of σ(t) as change points [14]. Shown through empirical analysis on both simulated and real data, we find this is insufficient.…”

“…Following previous works of [14] [21] [11] we use the area under the curve (CP-AUC) to evaluate change point performance. We also report the F1 score (CP-F1) for offline multiple CPD, [22] using a margin of error δ for the acceptable offset to the true label.…”

Easing Power Consumption of Wearable Activity Monitoring with Change Point Detection

“…For a random variable X defined In contrast, unsupervised methods look for changes in data. These changes can be a quantitative distance between states as with subspace modeling [47], membership in different clusters [48,49], or a distance value generated by a kernel function or a graph [50]. Alternatively, the probability of a change point can be computed using Bayes' theorem [51] or a Gaussian Process prediction [52].…”