Change Point Detection Research Articles

Automated selection of changepoints using empirical P-values and trimming

One challenge that arises when analyzing mobile health (mHealth) data is that updates to the proprietary algorithms that process these data can change apparent patterns. Since the timings of these updates are not publicized, an analytic approach is necessary to determine whether changes in mHealth data are due to lifestyle behaviors or algorithmic updates. Existing methods for identifying changepoints do not consider multiple types of changepoints, may require prespecifying the number of changepoints, and often involve nonintuitive parameters. We propose a novel approach, Automated Selection of Changepoints using Empirical P-values and Trimming (ASCEPT), to select an optimal set of changepoints in mHealth data. ASCEPT involves 2 stages: (1) identification of a statistically significant set of changepoints from sequential iterations of a changepoint detection algorithm; and (2) trimming changepoints within linear and seasonal trends. ASCEPT is available at https://github.com/matthewquinn1/changepointSelect. We demonstrate ASCEPT's utility using real-world mHealth data collected through the Precision VISSTA study. We also demonstrate that ASCEPT outperforms a comparable method, circular binary segmentation, and illustrate the impact when adjusting for changepoints in downstream analysis. ASCEPT offers a practical approach for identifying changepoints in mHealth data that result from algorithmic updates. ASCEPT's only required parameters are a significance level and goodness-of-fit threshold, offering a more intuitive option compared to other approaches. ASCEPT provides an intuitive and useful way to identify which changepoints in mHealth data are likely the result of updates to the underlying algorithms that process the data.

Seeded binary segmentation: a general methodology for fast and optimal changepoint detection

Summary We propose seeded binary segmentation for large-scale changepoint detection problems. We construct a deterministic set of background intervals, called seeded intervals, in which single changepoint candidates are searched for. The final selection of changepoints based on these candidates can be done in various ways, adapted to the problem at hand. The method is thus easy to adapt to many changepoint problems, ranging from univariate to high dimensional. Compared to recently popular random background intervals, seeded intervals lead to reproducibility and much faster computations. For the univariate Gaussian change in mean set-up, the methodology is shown to be asymptotically minimax optimal when paired with appropriate selection criteria. We demonstrate near-linear runtimes and competitive finite sample estimation performance. Furthermore, we illustrate the versatility of our method in high-dimensional settings.

Changepoint Detection: An Analysis of the Central England Temperature Series

Abstract This paper presents a statistical analysis of structural changes in the Central England temperature series, one of the longest surface temperature records available. A changepoint analysis is performed to detect abrupt changes, which can be regarded as a preliminary step before further analysis is conducted to identify the causes of the changes (e.g., artificial, human-induced, or natural variability). Regression models with structural breaks, including mean and trend shifts, are fitted to the series and compared via two commonly used multiple changepoint penalized likelihood criteria that balance model fit quality (as measured by likelihood) against parsimony considerations. Our changepoint model fits, with independent and short-memory errors, are also compared with a different class of models termed long-memory models that have been previously used by other authors to describe persistence features in temperature series. In the end, the optimal model is judged to be one containing a changepoint in the late 1980s, with a transition to an intensified warming regime. This timing and warming conclusion is consistent across changepoint models compared in this analysis. The variability of the series is not found to be significantly changing, and shift features are judged to be more plausible than either short- or long-memory autocorrelations. The final proposed model is one including trend shifts (both intercept and slope parameters) with independent errors. The analysis serves as a walk-through tutorial of different changepoint techniques, illustrating what can be statistically inferred.

Information Approach for Change Point Analysis of EGGAPE Distribution and Application to COVID-19 Data

The exponentiated generalized Gull alpha power exponential distribution is an extension of the exponential distribution that can model data characterized by various shapes of the hazard function. However, change point problem has not been studied for this distribution. In this study, the change point detection of the parameters of the exponentiated generalized Gull alpha power exponential distribution is studied using the modified information criterion. In addition, the binary segmentation procedure is used to identify multiple change point locations. The assumption is that all the parameters of the EGGAPE distributions are considered changeable. Simulation study is conducted to illustrate the power of the modified information criterion in detecting change point in the parameters with different sample sizes. Three applications related to COVID-19 data are used to demonstrate the applicability of the MIC in detecting change point in real life scenario.

Detecting changes in mixed‐sampling rate data sequences

AbstractDifferent environmental variables are often monitored using different sampling rates; examples include half‐hourly weather station measurements, daily data, and six‐day satellite data. Further when researchers want to combine the data into a single analysis this often requires data aggregation or down‐scaling. When one is seeking to identify changes within multivariate data, the aggregation and/or down‐scaling processes obscure the changes we seek. In this article, we propose a novel changepoint detection algorithm which can analyze multiple time series for co‐occurring changepoints with potentially different sampling rates, without requiring preprocessing to a standard sampling scale. We demonstrate the algorithm on synthetic data before providing an example identifying simultaneous changes in multiple variables at a location on the Greenland ice sheet using synthetic aperture radar and weather station data.

Change-Point detection for autocorrelated multivariate Poisson processes

ABSTRACT Statistical process control for count data has attracted increasing attention in recent years. The need for efficient control charts suitable for autocorrelated multivariate count processes is well recognized. However, there is a scarcity of research aiming to take into account the autocorrelation among the multivariate count data. We are motivated to study the Phase I analysis of autocorrelated multivariate Poisson processes to detect and estimate change points in reference datasets. A change-point method is proposed based on the multivariate Poisson INAR(1) model by integrating generalized likelihood ratio tests with the binary segmentation procedure. A diagnostic procedure for pinpointing the location of the change point is also discussed. Our simulation results show that the proposed method has a better performance than the benchmark method, across a range of possible shifts, in the detection effectiveness and diagnostic accuracy. Furthermore, a real example from the manufacturing industry is used to illustrate the implementation steps of the proposed method.

A real-time online unstart prediction approach for supersonic inlet

Unstart of supersonic inlet is an abnormal phenomenon, which may cause serious accidents such as flameouts. In this paper, we experimentally record the pressure signals from start to unstart at 25 different measurement points on the wall of a two-dimensional supersonic inlet under eight different experimental conditions. It can be found the existence of precursor phenomena by analyzing the pressure signals and schlieren image of the flow field. In order to detect precursor phenomena, a real-time online unstart prediction approach is proposed by combining change-point detection (CD), wavelet packet (WPT) and convolutional neural network (CNN), named CD-WPT-CNN in this paper, whose effectiveness is verified under two test conditions. In addition, we introduce three traditional real-time online unstart prediction methods and further confirm the superiority of CD-WPT-CNN for practical applications by comparing their performance in test conditions. All in all, the experimental results show that the proposed CD-WPT-CNN performs better in many respects and has a good application prospect.

Efficient multiple change point detection for high-dimensional generalized linear models.

Change point detection for high-dimensional data is an important yet challenging problem for many applications. In this paper, we consider multiple change point detection in the context of high-dimensional generalized linear models, allowing the covariate dimension p to grow exponentially with the sample size n. The model considered is general and flexible in the sense that it covers various specific models as special cases. It can automatically account for the underlying data generation mechanism without specifying any prior knowledge about the number of change points. Based on dynamic programming and binary segmentation techniques, two algorithms are proposed to detect multiple change points, allowing the number of change points to grow with n. To further improve the computational efficiency, a more efficient algorithm designed for the case of a single change point is proposed. We present theoretical properties of our proposed algorithms, including estimation consistency for the number and locations of change points as well as consistency and asymptotic distributions for the underlying regression coefficients. Finally, extensive simulation studies and application to the Alzheimer's Disease Neuroimaging Initiative data further demonstrate the competitive performance of our proposed methods.

Adaptive Partially Observed Sequential Change Detection and Isolation

ABSTRACT High-dimensional data has become popular due to the easy accessibility of sensors in modern industrial applications. However, one specific challenge is that it is often not easy to obtain complete measurements due to limited sensing powers and resource constraints. Furthermore, distinct failure patterns may exist in the systems, and it is necessary to identify the true failure pattern. This work focuses on the online adaptive monitoring of high-dimensional data in resource-constrained environments with multiple potential failure modes. To achieve this, we propose to apply the Shiryaev–Roberts procedure on the failure mode level and use the multi-arm bandit to balance the exploration and exploitation. We further discuss the theoretical property of the proposed algorithm to show that the proposed method can correctly isolate the failure mode. Finally, extensive simulations and two case studies demonstrate that the change point detection performance and the failure mode isolation accuracy can be greatly improved.

Multivariate change point detection for heterogeneous series

The multivariate change point detection problem has been encountered across various fields. Most approaches to this problem assume the series is homogeneous, i.e., all the coordinates change concurrently. Hence, the specific subset of the coordinates containing the change points cannot be determined. In this work, we propose S-MCPD, which is capable of detecting the position of multivariate change points for heterogeneous series by identifying specific coordinates of those changed. Specifically, the problem is discussed in the context of variable selection and transformed into the form of sparse group lasso. In simulation studies, we compared S-MCPD with four existing methods, inspect, sbs, dc, and cpm. The results showed that the performance of S-MCPD was comparable to that of inspect and was superior to other methods in terms of evaluation metrics. In addition, S-MCPD can determine not only the positions of change points, but also the subset of coordinates containing the change points, while other existing methods are unable to achieve this. Moreover, S-MCPD does not depend on the constant variance assumption and works quite well even when the covariance changes, which makes our method more practical. These are the two important contributions of our work. Finally, we applied S-MCPD to two real-world datasets to show its effectiveness.

Online change-point detection with kernels

Change-points in time series data are usually defined as the time instants at which changes in their properties occur. Detecting change-points is critical in a number of applications as diverse as detecting credit card and insurance frauds, or intrusions into networks. Recently the authors introduced an online kernel-based change-point detection method built upon direct estimation of the density ratio on consecutive time intervals. This paper further investigates this algorithm, making improvements and analyzing its behavior in the mean and mean square sense, in the absence and presence of a change point. These theoretical analyses are validated with Monte Carlo simulations. The detection performance of the algorithm is illustrated through experiments on real-world data and compared to state of the art methodologies.

Adaptive resources allocation CUSUM for binomial count data monitoring with application to COVID-19 hotspot detection

In this paper, we present an efficient statistical method (denoted as ‘Adaptive Resources Allocation CUSUM’) to robustly and efficiently detect the hotspot with limited sampling resources. Our main idea is to combine the multi-arm bandit (MAB) and change-point detection methods to balance the exploration and exploitation of resource allocation for hotspot detection. Further, a Bayesian weighted update is used to update the posterior distribution of the infection rate. Then, the upper confidence bound (UCB) is used for resource allocation and planning. Finally, CUSUM monitoring statistics to detect the change point as well as the change location. For performance evaluation, we compare the performance of the proposed method with several benchmark methods in the literature and showed the proposed algorithm is able to achieve a lower detection delay and higher detection precision. Finally, this method is applied to hotspot detection in a real case study of county-level daily positive COVID-19 cases in Washington State WA) and demonstrates the effectiveness with very limited distributed samples.

A taxonomy of surprise definitions

Surprising events trigger measurable brain activity and influence human behavior by affecting learning, memory, and decision-making. Currently there is, however, no consensus on the definition of surprise. Here we identify 18 mathematical definitions of surprise in a unifying framework. We first propose a technical classification of these definitions into three groups based on their dependence on an agent’s belief, show how they relate to each other, and prove under what conditions they are indistinguishable. Going beyond this technical analysis, we propose a taxonomy of surprise definitions and classify them into four conceptual categories based on the quantity they measure: (i) ‘prediction surprise’ measures a mismatch between a prediction and an observation; (ii) ‘change-point detection surprise’ measures the probability of a change in the environment; (iii) ‘confidence-corrected surprise’ explicitly accounts for the effect of confidence; and (iv) ‘information gain surprise’ measures the belief-update upon a new observation. The taxonomy poses the foundation for principled studies of the functional roles and physiological signatures of surprise in the brain.

The Mann-Kendall-Sneyers test to identify the change points of COVID-19 time series in the United States

BackgroundOne critical variable in the time series analysis is the change point, which is the point where an abrupt change occurs in chronologically ordered observations. Existing parametric models for change point detection, such as the linear regression model and the Bayesian model, require that observations are normally distributed and that the trend line cannot have extreme variability. To overcome the limitations of the parametric model, we apply a nonparametric method, the Mann-Kendall-Sneyers (MKS) test, to change point detection for the state-level COVID-19 case time series data of the United States in the early outbreak of the pandemic.MethodsThe MKS test is implemented for change point detection. The forward sequence and the backward sequence are calculated based on the new weekly cases between March 22, 2020 and January 31, 2021 for each of the 50 states. Points of intersection between the two sequences falling within the 95% confidence intervals are identified as the change points. The results are compared with two other change point detection methods, the pruned exact linear time (PELT) method and the regression-based method. Also, an open-access tool by Microsoft Excel is developed to facilitate the model implementation.ResultsBy applying the MKS test to COVID-19 cases in the United States, we have identified that 30 states (60.0%) have at least one change point within the 95% confidence intervals. Of these states, 26 states have one change point, 4 states (i.e., LA, OH, VA, and WA) have two change points, and one state (GA) has three change points. Additionally, most downward changes appear in the Northeastern states (e.g., CT, MA, NJ, NY) at the first development stage (March 23 through May 31, 2020); most upward changes appear in the Western states (e.g., AZ, CA, CO, NM, WA, WY) and the Midwestern states (e.g., IL, IN, MI, MN, OH, WI) at the third development stage (November 19, 2020 through January 31, 2021).ConclusionsThis study is among the first to explore the potential of the MKS test applied for change point detection of COVID-19 cases. The MKS test is characterized by several advantages, including high computational efficiency, easy implementation, the ability to identify the change of direction, and no assumption for data distribution. However, due to its conservative nature in change point detection and moderate agreement with other methods, we recommend using the MKS test primarily for initial pattern identification and data pruning, especially in large data. With modification, the method can be further applied to other health data, such as injuries, disabilities, and mortalities.

Bayesian modelling of piecewise trends and discontinuities to improve the estimation of coastal vertical land motion

One of the major sources of uncertainty affecting vertical land motion (VLM) estimations are discontinuities and trend changes. Trend changes are most commonly caused by seismic deformation, but can also stem from long-term (decadal to multidecadal) surface loading changes or from local origins. Although these issues have been extensively addressed for Global Navigation Satellite System (GNSS) data, there is limited knowledge of how such events can be directly detected and mitigated in VLM, derived from altimetry and tide-gauge differences (SATTG). In this study, we present a novel Bayesian approach to automatically and simultaneously detect such events, together with the statistics commonly estimated to characterize motion signatures. Next to GNSS time series, for the first time, we directly estimate discontinuities and trend changes in VLM data inferred from SATTG. We show that, compared to estimating a single linear trend, accounting for such variable velocities significantly increases the agreement of SATTG with GNSS values (on average by 0.36 mm/year) at 339 globally distributed station pairs. The Bayesian change point detection is applied to 606 SATTG and 381 GNSS time series. Observed VLM, which is identified as linear (i.e. where no significant trend changes are detected), has a substantially higher consistency with large-scale VLM effects of glacial isostatic adjustment (GIA) and contemporary mass redistribution (CMR). The standard deviation of SATTG (and GNSS) trend differences with respect to GIA+CMR trends is by 38% (and 48%) lower for time series with constant velocity compared to variable velocities. Given that in more than a third of the SATTG time series variable velocities are detected, the results underpin the importance to account for such features, in particular to avoid extrapolation biases of coastal VLM and its influence on relative sea-level-change determination. The Bayesian approach uncovers the potential for a better characterization of SATTG VLM changes on much longer periods and is widely applicable to other geophysical time series.

Novel Fractional Grey Prediction Model with the Change-Point Detection for Overseas Talent Mobility Prediction

Overseas students constitute the paramount talent resource for China, and, hence, overseas talent mobility prediction is crucial for the formulation of China’s talent strategy. This study proposes a new model for predicting the number of students studying abroad and returning students, based on the grey system theory, owing to the limited data and uncertainty of the influencing factors. The proposed model introduces change-point detection to determine the number of modeling time points, based on the fractional-order grey prediction model. We employed a change-point detection method to find the change points for determining the model length, based on the principle of new information priority, and used a fractional order accumulated generating operation to construct a grey prediction model. The two real data sets, the annual number of students studying abroad and returning students, were employed to verify the superiority of the proposed model. The results showed that the proposed model outperformed other benchmark models. Furthermore, the proposed model has been employed to predict the tendencies of overseas talent mobility in China by 2025. Further, certain policy recommendations for China’s talent strategy development have been proposed, based on the prediction results.

IADA: A dynamic interference-aware cloud scheduling architecture for latency-sensitive workloads

Cloud computing allows several applications to share physical resources, yielding rapid provisioning and improving hardware utilization. However, multiple applications contending for shared resources are susceptible to interference, which might lead to significant performance degradation and consequently an increase in Service Level Agreements violations. In previous work, we started to analyze resource contention and its impact on performance degradation and hardware utilization. Then, we created an interference-aware application classifier based on machine learning techniques and evaluated it comparing two classification strategies: (i) unique, when a single classification is performed over the entire applications’ execution; and (ii) segmented, when the classification is carried out over multiple static-defined intervals. Moving towards a dynamic scheduling solution, we combine and improve on previous work findings and, in this work, we present IADA, a full-fledged dynamic interference-aware cloud scheduling architecture for latency-sensitive workloads. Our approach consists in improving on a segmented interference classification of applications to a dynamic classification scheme based on workload variations. Aiming at using the available resource more efficiently and respecting Quality of Services requirements, the proposed architecture was developed supported by machine learning techniques, heuristics, and a bayesian changepoint detection algorithm for online inference. We conducted a set of real and simulated experiments, utilizing a developed extension of CloudSim Toolkit to analyze and compare the proposed architecture efficiency with related studies. Results evidenced that IADA reduces by 25%, on average, the overall performance degradation.

Online routing for smart electricity network under hybrid uncertainty

In this study, an online routing problem for the optimal power flow (OPF) of smart grids subject to forecasting errors and cyber-attacks on data integrity is investigated. Energy data packages and flow-dispatch commands are transmitted over a communication network and corrupted by adversaries. In particular, we consider false data injection attacks that maliciously tamper with the data presented to grid operators. We develop an OPF model considering piecewise invariable load and power generation, which can be evaluated using a linear program. We extend the problem to an online setting, where data are sequentially observed, and adaptive strategies are required to optimize a metric, called the regret function, over time. We then incorporate the state-of-the-art adaptive change-point detection approach to develop an online routing algorithm that retains a sublinear regret in both the time horizon and number of change points. The applicability and effectiveness of the proposed algorithm were verified by numerical experiments on real-world smart grids.

Identifying potential systemic changes in a regulated river: A diagnostic methodology based on whiteness property of innovation sequences

Traditional hydrologic routing schemes are structured in reference to a pre-assumed time-invariant inflow-storage-outflow function. In light of this, potential systemic changes, arising from river regulation, cannot be accommodated in such a static model structure. As such, a diagnostic methodology is developed in this study to examine the presence of potential systemic changes and recognize time spans in which the adopted inflow-storage-outflow function is inadequate to represent the functional behaviour of the system. This is done objectively by developing a two-step change-points detection algorithm based on the whiteness property of the innovation sequence. Using four carefully designed numerical experiments, our findings reveal that the proposed methodology (a) detects the non-stationary behaviour in streamflow time series associated with systemic changes objectively, (b) tracks the pathway of structural evolution of a hydrologic routing model properly, and (c) identifies time periods automatically wherein a river routing model structure needs to be updated.

An updated version of the ETAS model based on multiple change points detection

An updated version of the ETAS model based on multiple change points detection