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1. Finite Sample Change Point Inference and Identification for High-Dimensional Mean Vectors

   https://doi.org/10.1111/rssb.12406  

   Yu, Mengjia; Chen, Xiaohui (December 2020, Journal of the Royal Statistical Society Series B: Statistical Methodology)

   Abstract Cumulative sum (CUSUM) statistics are widely used in the change point inference and identification. For the problem of testing for existence of a change point in an independent sample generated from the mean-shift model, we introduce a Gaussian multiplier bootstrap to calibrate critical values of the CUSUM test statistics in high dimensions. The proposed bootstrap CUSUM test is fully data dependent and it has strong theoretical guarantees under arbitrary dependence structures and mild moment conditions. Specifically, we show that with a boundary removal parameter the bootstrap CUSUM test enjoys the uniform validity in size under the null and it achieves the minimax separation rate under the sparse alternatives when the dimension p can be larger than the sample size n. Once a change point is detected, we estimate the change point location by maximising the ℓ∞-norm of the generalised CUSUM statistics at two different weighting scales corresponding to covariance stationary and non-stationary CUSUM statistics. For both estimators, we derive their rates of convergence and show that dimension impacts the rates only through logarithmic factors, which implies that consistency of the CUSUM estimators is possible when p is much larger than n. In the presence of multiple change points, we propose a principled bootstrap-assisted binary segmentation (BABS) algorithm to dynamically adjust the change point detection rule and recursively estimate their locations. We derive its rate of convergence under suitable signal separation and strength conditions. The results derived in this paper are non-asymptotic and we provide extensive simulation studies to assess the finite sample performance. The empirical evidence shows an encouraging agreement with our theoretical results. 

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2. E-detectors: A Nonparametric Framework for Sequential Change Detection

   https://doi.org/10.51387/23-NEJSDS51  

   Shin, Jaehyeok; Ramdas, Aaditya; Rinaldo, Alessandro (January 2023, The New England Journal of Statistics in Data Science)

   Sequential change detection is a classical problem with a variety of applications. However, the majority of prior work has been parametric, for example, focusing on exponential families. We develop a fundamentally new and general framework for sequential change detection when the pre- and post-change distributions are nonparametrically specified (and thus composite). Our procedures come with clean, nonasymptotic bounds on the average run length (frequency of false alarms). In certain nonparametric cases (like sub-Gaussian or sub-exponential), we also provide near-optimal bounds on the detection delay following a changepoint. The primary technical tool that we introduce is called an e-detector, which is composed of sums of e-processes—a fundamental generalization of nonnegative supermartingales—that are started at consecutive times. We first introduce simple Shiryaev-Roberts and CUSUM-style e-detectors, and then show how to design their mixtures in order to achieve both statistical and computational efficiency. Our e-detector framework can be instantiated to recover classical likelihood-based procedures for parametric problems, as well as yielding the first change detection method for many nonparametric problems. As a running example, we tackle the problem of detecting changes in the mean of a bounded random variable without i.i.d. assumptions, with an application to tracking the performance of a basketball team over multiple seasons. 

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3. Distributionally Robust Quickest Change Detection using Wasserstein Uncertainty Sets

   Xie, Liyan; Liang, Yuchen; Veeravalli, Venugopal V (May 2024, PMLR)

   Dasgupta, Sanjoy; Mandt, Stephan; Li, Yingzhen (Ed.)

   The problem of quickest detection of a change in the distribution of streaming data is considered. It is assumed that the pre-change distribution is known, while the only information about the post-change is through a (small) set of labeled data. This post-change data is used in a data-driven minimax robust framework, where an uncertainty set for the post-change distribution is constructed. The robust change detection problem is studied in an asymptotic setting where the mean time to false alarm goes to infinity. It is shown that the least favorable distribution (LFD) is an exponentially tilted version of the pre-change density and can be obtained efficiently. A Cumulative Sum (CuSum) test based on the LFD, which is referred to as the distributionally robust (DR) CuSum test, is then shown to be asymptotically robust. The results are extended to the case with multiple post-change uncertainty sets and validated using synthetic and real data examples. 

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4. Quantifying input data drift in medical machine learning models by detecting change-points in time-series data

   https://doi.org/10.1117/12.3008771  

   Prathapan, Smriti; Samala, Ravi K; Hadjiyski, Nathan; D’Haese, Pierre-François; Maldonado, Fabien; Nguyen, Phuong; Yesha, Yelena; Sahiner, Berkman (April 2024, SPIE)

   Astley, Susan M; Chen, Weijie (Ed.)

   Devices enabled by artificial intelligence (AI) and machine learning (ML) are being introduced for clinical use at an accelerating pace. In a dynamic clinical environment, these devices may encounter conditions different from those they were developed for. The statistical data mismatch between training/initial testing and production is often referred to as data drift. Detecting and quantifying data drift is significant for ensuring that AI model performs as expected in clinical environments. A drift detector signals when a corrective action is needed if the performance changes. In this study, we investigate how a change in the performance of an AI model due to data drift can be detected and quantified using a cumulative sum (CUSUM) control chart. To study the properties of CUSUM, we first simulate different scenarios that change the performance of an AI model. We simulate a sudden change in the mean of the performance metric at a change-point (change day) in time. The task is to quickly detect the change while providing few false-alarms before the change-point, which may be caused by the statistical variation of the performance metric over time. Subsequently, we simulate data drift by denoising the Emory Breast Imaging Dataset (EMBED) after a pre-defined change-point. We detect the change-point by studying the pre- and post-change specificity of a mammographic CAD algorithm. Our results indicate that with the appropriate choice of parameters, CUSUM is able to quickly detect relatively small drifts with a small number of false-positive alarms. 

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5. Change Point Models for Real-time V2I Cyber Attack Detection in a Connected Vehicle Environment

   Comert, G. (January 2019, Transportation Research Board Annual Meeting 2019)

   Connected vehicle (CV) systems are cognizant of potential cyber attacks because of increasing connectivity between its different components such as vehicles, roadside infrastructure and traffic management centers. However, it is a challenge to detect security threats in real-time and develop appropriate/effective countermeasures for a CV system because of the dynamic behavior of such attacks, high computational power requirement and a historical data requirement for training detection models. To address these challenges, statistical models, especially change point models, have potentials for real-time anomaly detections. Thus, the objective of this study is to investigate the efficacy of two change point models, Expectation Maximization (EM) and two forms of Cumulative Summation (CUSUM) algorithms (i.e., typical and adaptive), for real-time V2I cyber attack detection in a CV Environment. To prove the efficacy of these models, we evaluated these two models for three different type of cyber attack, denial of service (DOS), impersonation, and false information, using basic safety messages (BSMs) generated from CVs through simulation. Results from numerical analysis revealed that EM, CUSUM, and adaptive CUSUM could detect these cyber attacks, DOS, impersonation, and false information, with an accuracy of (99\%, 100\%, 100\%), (98\%, 100\%, 100\%), and (100\%, 98\%, 100\%) respectively. 

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