Change-point detection in the marginal distribution of a linear process

In this study, the Student’s t parametric and Mann-Whitney nonparametric change point models (CPMs) were applied to detect change point in the annual Persian Gulf sea surface temperature anomalies (PGSSTA) time series for the period 1951–2013. The PGSSTA time series, which were serially correlated, were transformed to produce an uncorrelated pre-whitened time series. The pre-whitened PGSSTA time series were utilized as the input file of change point models. Both the applied parametric and nonparametric CPMs estimated the change point in the PGSSTA in 1992. The PGSSTA follow the normal distribution up to 1992 and thereafter, but with a different mean value after year 1992. The estimated slope of linear trend in PGSSTA time series for the period 1951–1992 was negative; however, that was positive after the detected change point. Unlike the PGSSTA, the applied CPMs suggested no change point in the Nino3.4SSTA time series.

Many modern applications require detecting change points in complex sequential data. Most existing methods for change point detection used in streaming data settings are unsupervised and, as a consequence, lack any information regarding what kind of changes we want to detect or if some kinds of changes are safe to ignore. This often results in poor change detection performance, as many spurious changes are falsely detected as change points. We present a novel change point detection framework that uses a small number of labeled change point instances as supervision for learning a ground metric such that Sinkhorn divergences can be then used in two-sample tests on sliding windows to detect change points. Our method can be used to learn a sparse metric which can be useful for both feature selection and interpretation in high-dimensional change point detection settings. Experiments on simulated as well as real world sequences show that our proposed method can substantially improve change point detection performance over existing unsupervised change point detection methods using only few labeled change point instances.

Modern industrial assets (e.g., generators, turbines, engines) are outfitted with numerous sensors to monitor key operating and environmental variables. Unusual sensor readings, such as high temperature, excessive vibration, or low current, could trigger rule-based actions (also known as faults) that range from warning alarms to immediate shutdown of the asset to prevent potential damage. In the case study of this article, a wind park experienced a sudden surge in vibration-induced shutdowns. We utilize fault data logs from the park with the goal of detecting common change points across turbines. Another important goal is the localization of fault occurrences to an identifiable set of turbines. The literature on change point detection and localization for multiple assets is highly sparse. Our technical development is based on the generalized linear modeling framework. We combine well-known solutions to change point detection for a single asset with a heuristics-based approach to identify a common change point(s) for multiple assets. The performance of the proposed detection and localization algorithms is evaluated through synthetic (Monte Carlo) fault data streams. Several novel performance metrics are defined to characterize different aspects of a change point detection algorithm for multiple assets. For the case study example, the proposed methodology identified the change point and the subset of affected turbines with a high degree of accuracy. The problem described here warrants further study to accommodate general fault distributions, change point detection algorithms, and very large fleet sizes.

Change point analysis of mean annual air temperature in Iran

Environmental health studies are of great interest in research to evaluate the mortality-temperature relationship by adjusting spatially correlated random effects as well as identifying significant change points in temperature. However, this relationship is often not expressed using parametric models, which makes identifying change points an even more challenging problem. This paper proposes a unified semiparametric approach to simultaneously identify the nonlinear mortality-temperature relationship and detect spatially-dependent change points. A unified method is proposed for the model estimation, spatially dependent change points detection, and testing whether they are significant simultaneously by a permutation-based test. We operate under the assumption that change points remain constant, yet acknowledge the uncertainty regarding their precise number. These change points are influenced by the smoothing of an unknown function, which in turn relies on a smoothing variable and spatial random effects. Consequently, the detection of change points may be influenced by spatial effects. In this paper, several simulation studies are conducted to evaluate the performance of our proposed approach. The advantages of this unified approach are demonstrated using epidemiological data on mortality and temperature.

With improvements to cancer diagnoses and treatments, incidences and mortality rates have changed. However, the most commonly used analysis methods do not account for such distributional changes. In survival analysis, change point problems can concern a shift in a distribution for a set of time‐ordered observations, potentially under censoring or truncation. We propose a sequential testing approach for detecting multiple change points in the Weibull accelerated failure time model, since this is sufficiently flexible to accommodate increasing, decreasing, or constant hazard rates and is also the only continuous distribution for which the accelerated failure time model can be reparameterized as a proportional hazards model. Our sequential testing procedure does not require the number of change points to be known; this information is instead inferred from the data. We conduct a simulation study to show that the method accurately detects change points and estimates the model. The numerical results along with real data applications demonstrate that our proposed method can detect change points in the hazard rate.

Sliding window change point detection based dynamic network model inference framework for airport ground service process

Capturing correlation changes by applying kernel change point detection on the running correlations

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.

In this dissertation a new model for the description of cell organelle movement is defined and a test and change point detection algorithm for changes in the model parameters is proposed. The description of movement patterns can be important for the understanding of various biological processes on multiple scales. One of the primary goals is to understand the causes of change between movement patterns. On the micro scale, movement patterns of cell organelles and swimming micro-organisms such as cells are investigated. To learn more about the different movement types of cell organelles, as well as the changes between these types, we analyse the movement of two specific types of cell organelles in the root of the plant Arabidopsis thaliana, Plastids and Peroxisomes. Interestingly, while all tracks were recorded in three dimensions, over 90% of the tracks show more than 95% of their movement variability in only two dimensions. We therefore focus on the two-dimensional projection of the movements, allowing comparability to approaches for animal movement pattern analysis. In this data set of organelle movement we observe visually prominent, linear movement structures with seemingly piecewise constant movement direction and speed. Since the different sections of the movement could be associated with different movement mechanisms such as movement through cytoplasmic streaming or transport along intracellular filaments, it is of interest to detect the change points (CPs) in the direction and speed of the movement. The most widely used time discrete models are variants of the random walk. Most often used, particularly in animal studies, are so-called correlated random walks, which are parametrised by a random turning angle relative to the previous direction. Correlated random walks are useful to model movement where the difference between highly directed and undirected movement is of interest. By fitting HMM models to the observed organelle movement we show that a biased random walk (BRW), parametrised via absolute directions, may be more appropriate to model sections of different but constant movement direction. The BRW is therefore used as a reference model. However, our findings indicate that a BRW shows a higher variability in the movement direction and may thus move less strictly along a linear structure than can be observed in many organelle tracks. Therefore, we define a new model termed linear walk (LW) with less variability around an expected position. Both models, the BRW and LW, have the same process of expected positions, which is parametrised by two parameters, the movement direction and the step length, where the direction is the angle relative to the x-axis. The models differ in regard to the variability around the expected position. In the BRW, independent random increments are summed up, while in the LW an independent, random error is added to each expected position. Due to this definition the changes in movement direction and step length can be described independently. The expectation of the increments in both models can be parameterised by the movement direction and step length or alternatively by a two dimensional expectation. The maximum likelihood estimators of the model parameters in both models and proof of their strong consistency is provided. Note that for the expectation of the increments in the BRW the estimator is the classical mean, while in the LW the estimator is a weighted average. In the context of the BRW model a known MOSUM approach for the bivariate detection of change points is easily adapted to our setting. In this approach a double window is shifted over the movement track. The difference of the bivariate expectation of increments in the left and right window half is estimated, leading to a process of differences that fluctuates around the origin, but shows systematic deviation in the neighborhood around a CP. Therefore the maximum deviation of the process of differences from the origin is used as a test statistic. The rejection threshold is obtained via simulation of a limit process. CPs are estimated successively by identifying local deviations of the process of differences from the origin. In the LW model the MOSUM has inconvenient properties due to the dependency structure of the increments. Therefore a moving kernel approach is proposed where the maximum likelihood estimators for the expectation in the LW model are used instead of the classical mean. For this approach the proof of the weak convergence of the process of differences assuming the true variance is provided. For both approaches simulation studies concerning the test power and precision are provided. Since the CPs in both approaches are detected within the expectation, we propose a graphical technique to classify the detected change points into CPs in movement direction and step length and apply this technique to the observed organelle movement.

Economic system mathematical model often contains multiple variance change points about structure model. In the same mean, we combine the Bayesian method with the maximum likelihood method on the detection of the variance multiple change points. With Bayesian method, we can eliminate extra parameters first, and then use maximum likelihood method to find the change position. So we both can eliminate extra parameters and can avoid the change point on the prior distribution unknown problem. In addition, the benefit of the maximum likelihood method is just needed to find out likelihood density function of the maximal solution in the solution space, thus the variance of multiple change point detection problem is resolved. By making substantial analysis with an example from commodity house prices in Wuhan, three changes of variance are found in all. They correspond to the major structure changes of contemporary property market in Wuhan city. The method is practical and effective as the final results shown. It also has a certain practical significance.

MotivationConventional identification methods for gene regulatory networks (GRNs) have overwhelmingly adopted static topology models, which remains unchanged over time to represent the underlying molecular interactions of a biological system. However, GRNs are dynamic in response to physiological and environmental changes. Although there is a rich literature in modeling static or temporally invariant networks, how to systematically recover these temporally changing networks remains a major and significant pressing challenge. The purpose of this study is to suggest a two-step strategy that recovers time-varying GRNs.ResultsIt is suggested in this paper to utilize a switching auto-regressive model to describe the dynamics of time-varying GRNs, and a two-step strategy is proposed to recover the structure of time-varying GRNs. In the first step, the change points are detected by a Kalman-filter based method. The observed time series are divided into several segments using these detection results; and each time series segment belonging to two successive demarcating change points is associated with an individual static regulatory network. In the second step, conditional network structure identification methods are used to reconstruct the topology for each time interval. This two-step strategy efficiently decouples the change point detection problem and the topology inference problem. Simulation results show that the proposed strategy can detect the change points precisely and recover each individual topology structure effectively. Moreover, computation results with the developmental data of Drosophila Melanogaster show that the proposed change point detection procedure is also able to work effectively in real world applications and the change point estimation accuracy exceeds other existing approaches, which means the suggested strategy may also be helpful in solving actual GRN reconstruction problem.

In this article, we consider change point inference for high dimensional linear models.For change point detection, given any subgroup of variables, we propose a new method for testing the homogeneity of corresponding regression coefficients across the observations.Under some regularity conditions, the proposed new testing procedure controls the type I error asymptotically and is powerful against sparse alternatives and enjoys certain optimality.For change point identification, an "argmax" based change point estimator is proposed which is shown to be consistent for the true change point location.Moreover, combining with the binary segmentation technique, we further extend our new method for detecting and identifying multiple change points.Extensive numerical studies justify the validity of our new method and demonstrate its competitive performance.

Photovoltaic (PV) soiling profiles exhibit a sawtooth shape, where cleaning events and soiling deposition periods alternate. Generally, the rate at which soiling accumulates is assumed to be constant within each deposition period. In reality, changes in rates can occur because of sudden variations in climatic conditions, e.g., dust storms or prolonged periods of rain. The existing models used to extract the soiling profile from the PV performance data might fail to capture the change points and occasionally estimate incorrect soiling profiles. This work analyzes how the introduction of change points can be beneficial for soiling extraction. Data from nine soiling stations and a 1-MW site were analyzed by using piecewise regression and three change point detection algorithms. The results showed that accounting for change points can provide significant benefits to the modeling of soiling even if not all the change point algorithms return the same improvements. Considering change points in historical trends is found to be particularly important for studies aiming to optimize cleaning schedules.

The detection of change points is a pivotal task in statistical analysis. In the quantum realm, it is a new primitive where one aims at identifying the point where a source that supposedly prepares a sequence of particles in identical quantum states starts preparing a mutated one. We obtain the optimal procedure to identify the change point with certainty-naturally at the price of having a certain probability of getting an inconclusive answer. We obtain the analytical form of the optimal probability of successful identification for any length of the particle sequence. We show that the conditional success probabilities of identifying each possible change point show an unexpected oscillatory behavior. We also discuss local (online) protocols and compare them with the optimal procedure.