Sequential Change-point Detection Research Articles

Sequential change-point detection in time series models with conditional heteroscedasticity

In this study, we investigate a sequential procedure for the early detection of parameter changes in conditionally heteroscedastic time series models. We introduce the detectors based on the cumulative sum of score vectors and residuals for this procedure. The asymptotic properties of the monitoring procedures are established under the null and alternative hypotheses. Simulation results are provided for illustration.

A series expansion formula of the scale matrix with applications in CUSUM analysis

We introduce a new Lévy fluctuation theoretic method to analyze the cumulative sum (CUSUM) procedure in sequential change-point detection. When observations are phase-type distributed and the post-change distribution is given by exponential tilting of its pre-change distribution, the first passage analysis of the CUSUM statistic is reduced to that of a certain Markov additive process. We develop a novel series expansion formula of the scale matrix for Markov additive processes of finite activity, and apply it to derive exact expressions of the average run length, average detection delay, and false alarm probability under the CUSUM procedure.

Sequential label shift detection in classification data: An application to dengue fever.

Classifiers have been developed to help diagnose dengue fever in patients presenting with febrile symptoms. However, classifier predictions often rely on the assumption that new observations come from the same distribution as training data. If the population prevalence of dengue changes, as would happen with a dengue outbreak, it is important to raise an alarm as soon as possible, so that appropriate public health measures can be taken and also so that the classifier can be re-calibrated. In this paper, we consider the problem of detecting such a change in distribution in sequentially-observed, unlabeled classification data. We focus on label shift changes to the distribution, where the class priors shift but the class conditional distributions remain unchanged. We reduce this problem to the problem of detecting a change in the one-dimensional classifier scores, leading to simple nonparametric sequential changepoint detection procedures. Our procedures leverage classifier training data to estimate the detection statistic, and converge to their parametric counterparts in the size of the training data. In simulated outbreaks with real dengue data, we show that our method outperforms other detection procedures in this label shift setting.

Truncated sequential change-point detection for Markov chains with applications in the epidemic statistical analysis

In this study, we consider disorder detection problems for statistical models with dependent observations defined by Markov chains in a Bayesian setting for a uniform prior distribution when the number of observations is limited by some known quantity. To achieve this, a new optimal sequential detection procedure is constructed using optimal stopping methods. This procedure minimizes the average delay time in the class of sequential procedures with false alarm probabilities that do not exceed a fixed value. The main difference between the proposed detection procedure and the conventional ones is that it is based not on the posterior probabilities but on the weighted Shiryaev-Roberts statistic. This allows for optimal detection in a nonasymptotic sense over any bounded time interval. Thereafter, we applied the constructed procedures to the early detection problem for the beginning of the epidemic spread. We used two epidemic models: the binomial model proposed by Baron, Choudhary, and Yu (2013) and the model based on the Gaussian approximation introduced by Pergamenchtchikov, Tartakovsky, and Spivak (2022). The theoretical results were confirmed through numerical simulations using the Monte Carlo method.

A note on online change point detection

We investigate sequential change point estimation and detection in univariate nonparametric settings, where a stream of independent observations from sub-Gaussian distributions with a common variance factor and piecewise-constant but otherwise unknown means are collected. We develop a simple CUSUM-based methodology that provably control the probability of false alarms or the average run length while minimizing, in a minimax sense, the detection delay. We allow for all the model parameters to vary in order to capture a broad range of levels of statistical hardness for the problem at hand. We further show how our methodology is applicable to the case in which multiple change points are to be estimated sequentially.

Real-time change point detection in linear models using the ranking selection procedure

We propose a novel sequential change point detection method in linear models. Our method uses a given historical data set to determine the prechange model. Significant features are selected using the ranking procedure, which is an innovative approach aimed at revealing the rank of all features in terms of their effects on the model. We establish the asymptotic properties of the test statistic under the null and alternative hypotheses. Simulations are conducted to illustrate the performance of the proposed method. We conclude with a real data application to illustrate the detection procedure.

Compound Sequential Change-point Detection in Parallel Data Streams

We consider sequential change-point detection in parallel data streams, where each stream has its own change point. Once a change is detected in a data stream, this stream is deactivated permanently. The goal is to maximize the normal operation of the pre-change streams, while controlling the proportion of post-change streams among the active streams at all time points. Taking a Bayesian formulation, we develop a compound decision framework for this problem. A procedure is proposed that is uniformly optimal among all sequential procedures which control the expected proportion of post-change streams at all time points. We also investigate the asymptotic behavior of the proposed method when the number of data streams grows large. Numerical examples are provided to illustrate the use and performance of the proposed method.

Sequential Change Point Detection for Time Series - An Adjusted-Range Based Approach

Sequential Change Point Detection for Time Series - An Adjusted-Range Based Approach

Sequential change-point detection for skew normal distribution

In this article, we propose a modified max-cumulative sum (CUSUM) procedure for detecting changes in parameters of skew normal distribution. The corresponding false alarms frequency and the postchange detection delay are investigated. Asymptotic behaviors of detection delay and theoretical optimality of the detection procedure have been established. Simulations have been conducted to show the performance of the proposed method and compare it to the other existing methods including CUSUM. Real data are given to illustrate the detection procedure.

Bandit Change-Point Detection for Real-Time Monitoring High-Dimensional Data Under Sampling Control

In many real-world problems of real-time monitoring high-dimensional streaming data, one wants to detect an undesired event or change quickly once it occurs, but under the sampling control constraint in the sense that one might be able to only observe or use selected components data for decision-making per time step in the resource-constrained environments. In this article, we propose to incorporate multi-armed bandit approaches into sequential change-point detection to develop an efficient bandit change-point detection algorithm based on the limiting Bayesian approach to incorporate a prior knowledge of potential changes. Our proposed algorithm, termed Thompson-Sampling-Shiryaev-Roberts-Pollak (TSSRP), consists of two policies per time step: the adaptive sampling policy applies the Thompson Sampling algorithm to balance between exploration for acquiring long-term knowledge and exploitation for immediate reward gain, and the statistical decision policy fuses the local Shiryaev–Roberts–Pollak statistics to determine whether to raise a global alarm by sum shrinkage techniques. Extensive numerical simulations and case studies demonstrate the statistical and computational efficiency of our proposed TSSRP algorithm.

Sequential Change-Point Detection for Mutually Exciting Point Processes

We present a new CUSUM procedure for sequential change-point detection in self- and mutually-exciting point processes (specifically, Hawkes networks) using discrete events data. Hawkes networks have become a popular model in statistics and machine learning, primarily due to their capability in modeling irregularly observed data where the timing between events carries a lot of information. The problem of detecting abrupt changes in Hawkes networks arises from various applications, including neuroengineering, sensor networks, and social network monitoring. Despite this, there has not been an efficient online algorithm for detecting such changes from sequential data. To this end, we propose an online recursive implementation of the CUSUM statistic for Hawkes processes, which is computationally and memory-efficient and can be decentralized for distributed computing. We first prove theoretical properties of this new CUSUM procedure, then show the improved performance of this approach over existing methods, including the Shewhart procedure based on count data, the generalized likelihood ratio statistic, and the standard score statistic. This is demonstrated via simulation studies and an application to population code change-detection in neuroengineering.

Sequential changepoint detection in neural networks with checkpoints

We introduce a framework for online changepoint detection and simultaneous model learning which is applicable to highly parametrized models, such as deep neural networks. It is based on detecting changepoints across time by sequentially performing generalized likelihood ratio tests that require only evaluations of simple prediction score functions. This procedure makes use of checkpoints, consisting of early versions of the actual model parameters, that allow to detect distributional changes by performing predictions on future data. We define an algorithm that bounds the Type I error in the sequential testing procedure. We demonstrate the efficiency of our method in challenging continual learning applications with unknown task changepoints, and show improved performance compared to online Bayesian changepoint detection.

Minimax and pointwise sequential changepoint detection and identification for general stochastic models

This paper considers the problem of joint change detection and identification assuming multiple composite post-change hypotheses. We propose a multihypothesis changepoint detection-identification procedure that controls the probabilities of false alarm and wrong identification. We show that the proposed procedure is asymptotically minimax and pointwise optimal, minimizing moments of the detection delay as probabilities of false alarm and wrong identification approach zero. The asymptotic optimality properties hold for general stochastic models with dependent and nonidentically distributed observations. We illustrate general results for detection-identification of changes in multistream Markov ergodic processes. We consider several examples, including an application to rapid detection-identification of COVID-19 in Italy. Our proposed sequential algorithm allows much faster detection of COVID-19 than standard methods.

Inference for nonstationary time series of counts with application to change-point problems

We consider an integer-valued time series \((Y_t)_{t\in {\mathbb {Z}}}\) where the model after a time \(k^*\) is Poisson autoregressive with the conditional mean that depends on a parameter \(\theta ^*\in \varTheta \subset {\mathbb {R}}^d\). The structure of the process before \(k^*\) is unknown; it could be any other integer-valued process, that is, \((Y_t)_{t\in {\mathbb {Z}}}\) could be nonstationary. It is established that the maximum likelihood estimator of \(\theta ^*\) computed on the nonstationary observations is consistent and asymptotically normal. Subsequently, we carry out the sequential change-point detection in a large class of Poisson autoregressive models, and propose a monitoring scheme for detecting change. The procedure is based on an updated estimator, which is computed without the historical observations. The above results of inference in a nonstationary setting are applied to prove the consistency of the proposed procedure. A simulation study as well as a real data application are provided.

Sequential change point detection in high dimensional time series

Change point detection in high dimensional data has found considerable interest in recent years. Most of the literature either designs methodology for a retrospective analysis, where the whole sample is already available when the statistical inference begins, or considers online detection schemes controlling the average time until a false alarm. This paper takes a different point of view and develops monitoring schemes for the online scenario, where high dimensional data arrives successively and the goal is to detect changes as fast as possible controlling at the same time the probability of a type I error of a false alarm. We develop a sequential procedure capable of detecting changes in the mean vector of a successively observed high dimensional time series with spatial and temporal dependence. The statistical properties of the method are analyzed in the case where both, the sample size and dimension tend to infinity. In this scenario, it is shown that the new monitoring scheme has asymptotic level alpha under the null hypothesis of no change and is consistent under the alternative of a change in at least one component of the high dimensional mean vector. The approach is based on a new type of monitoring scheme for one-dimensional data which turns out to be often more powerful than the usually used CUSUM and Page-CUSUM methods, and the component-wise statistics are aggregated by the maximum statistic. For the analysis of the asymptotic properties of our monitoring scheme we prove that the range of a Brownian motion on a given interval is in the domain of attraction of the Gumbel distribution, which is a result of independent interest in extreme value theory. The finite sample properties of the new methodology are illustrated by means of a simulation study and in the analysis of a data example.

Online Change Point Detection for Weighted and Directed Random Dot Product Graphs

Given a sequence of random (directed and weighted) graphs, we address the problem of online monitoring and detection of changes in the underlying data distribution. Our idea is to endow sequential change-point detection (CPD) techniques with a graph representation learning substrate based on the versatile Random Dot Product Graph (RDPG) model. We consider efficient, online updates of a judicious monitoring function, which quantifies the discrepancy between the streaming graph observations and the nominal RDPG. This reference distribution is inferred via spectral embeddings of the first few graphs in the sequence. We characterize the distribution of this running statistic to select thresholds that guarantee error-rate control, and under simplifying approximations we offer insights on the algorithm’s detection resolution and delay. The end result is a lightweight online CPD algorithm, that is also explainable by virtue of the well-appreciated interpretability of RDPG embeddings. This is in stark contrast with most existing graph CPD approaches, which either rely on extensive computation, or they store and process the entire observed time series. An apparent limitation of the RDPG model is its suitability for undirected and unweighted graphs only, a gap we aim to close here to broaden the scope of the CPD framework. Unlike previous proposals, our non-parametric RDPG model for weighted graphs does not require a priori specification of the weights’ distribution to perform inference and estimation. This network modeling contribution is of independent interest beyond CPD. We offer an open-source implementation of the novel online CPD algorithm for weighted and direct graphs, whose effectiveness and efficiency are demonstrated via (reproducible) synthetic and real network data experiments.

Corrections to “Sequential Change-Point Detection for High-Dimensional and Non-Euclidean Data”

Corrections to “Sequential Change-Point Detection for High-Dimensional and Non-Euclidean Data”

Sequential Change-Point Detection for High-Dimensional and Non-Euclidean Data

In many applications, it is often of practical and scientific interest to detect anomaly events in a streaming sequence of high-dimensional or non-Euclidean observations. We study a non-parametric framework that utilizes nearest neighbor information among the observations to detect changes in an online setting. It can be applied to data in arbitrary dimension and non-Euclidean data as long as a similarity measure on the sample space can be defined. We consider new test statistics under this framework that can detect anomaly events more effectively than the existing test while keeping the false discovery rate controlled at a fixed level. Analytic formulas approximating the average run lengths of the new approaches are derived to make them fast applicable to modern datasets. Simulation studies are provided to support theoretical results. The proposed approach is illustrated with an analysis of the NYC taxi dataset.

On Covert Communication Against Sequential Change-Point Detection

We investigate covert communication under a sequential change-point detection (SCPD) framework, where a transmitter, Alice, attempts to communicate reliably with a receiver, Bob, over an additive white Gaussian noise channel, while simultaneously ensuring covertness (low probability of detection) with respect to an adversary, Willie. Different from the binary hypothesis test based detection framework considered in prior works where Willie collects all signal samples together and makes a decision in a batch manner, we view Willie’s detection process as an SCPD process that works in a real-time manner. We establish a new criterion to evaluate the covertness of the communication between Alice and Bob, and investigate the performance of covert communication accordingly. Subject to the proposed constraint on covertness, we investigate the feasible transmit power and transmission duration under three SCPD algorithms, namely, the Shewhart test, the finite moving average chart (FMAC), and the cumulative sum (CUSUM) test, and characterize how the covert communication throughput scales with the average run length to false alarm (ARL2FA) of Willie’s detector as the ARL2FA increases without bound. Our theoretical results can be viewed as upper bounds on the covert communication throughput that can be achieved, and we show that compared with the case where Willie performs the CUSUM test, Alice and Bob achieve a higher covert communication throughput if Willie performs the Shewhart test or the FMAC.

Detection and identification of changes of hidden Markov chains: asymptotic theory

This paper revisits a unified framework of sequential change-point detection and hypothesis testing modeled using hidden Markov chains and develops its asymptotic theory. Given a sequence of observations whose distributions are dependent on a hidden Markov chain, the objective is to quickly detect critical events, modeled by the first time the Markov chain leaves a specific set of states, and to accurately identify the class of states that the Markov chain enters. We propose computationally tractable sequential detection and identification strategies and obtain sufficient conditions for the asymptotic optimality in two Bayesian formulations. Numerical examples are provided to confirm the asymptotic optimality.