Location Of Change Points Research Articles

Detecting linear trend changes in data sequences

We propose TrendSegment, a methodology for detecting multiple change-points corresponding to linear trend changes in one dimensional data. A core ingredient of TrendSegment is a new Tail-Greedy Unbalanced Wavelet transform: a conditionally orthonormal, bottom-up transformation of the data through an adaptively constructed unbalanced wavelet basis, which results in a sparse representation of the data. Due to its bottom-up nature, this multiscale decomposition focuses on local features in its early stages and on global features next which enables the detection of both long and short linear trend segments at once. To reduce the computational complexity, the proposed method merges multiple regions in a single pass over the data. We show the consistency of the estimated number and locations of change-points. The practicality of our approach is demonstrated through simulations and two real data examples, involving Iceland temperature data and sea ice extent of the Arctic and the Antarctic. Our methodology is implemented in the R package trendsegmentR, available from CRAN.

Extending Beyond Bagust and Beale: Fully Parametric Piecewise Exponential Models for Extrapolation of Survival Outcomes in Health Technology Assessment

ObjectivesWhen extrapolating time-to-event data the Bagust and Beale (B&B) approach uses the Kaplan-Meier survival function until a manually chosen time point, after which a constant hazard is assumed. This study demonstrates an objective statistical approach to estimate this time point. MethodsWe estimate piecewise exponential models (PEMs), whereby the hazard function is partitioned into segments each with constant hazards. The boundaries of these segments are known as change points. Our approach determines the location and number of change points in PEMs from which the hazard in the final segment is used to model long-term survival. We reviewed previous applications of the B&B approach in National Institute for Health and Care Excellence Technology Appraisals (TAs) completed between July 2011 and June 2017. The time points after which constant hazards were assumed were compared between PEMs and the B&B approaches. When further survival data were published following the original TA, we compared these updated estimates to predicted survival from the PEM and other parametric models adjusted for general population mortality. ResultsSix of the 59 TAs in this review considered the B&B approach. There was general agreement between the location of time points identified through the PEM and the B&B approaches. In 2 of the identified TAs the best fitting model to the data was a no-change-point model. Of the 3 TAs for which further survival data became available, PEM provided the closest prediction for survival outcomes in 2 TAs. ConclusionsPEMs are useful for survival extrapolation when a long-term constant hazard trend for the disease is clinically plausible.

A sequential Bayesian changepoint detection procedure for aberrant behaviours in computerized testing.

Changepoints are abrupt variations in a sequence of data in statistical inference. In educational and psychological assessments, it is essential to properly differentiate examinees' aberrant behaviours from solution behaviour to ensure test reliability and validity. In this paper, we propose a sequential Bayesian changepoint detection algorithm to monitor the locations of changepoints for response times in real time and, subsequently, further identify types of aberrant behaviours in conjunction with response patterns. Two simulation studies were conducted to investigate the efficiency and accuracy of the proposed detection procedure in terms of identifying one or multiple changepoints at different locations. In addition to manipulating the number and locations of changepoints, two types of aberrant behaviours were also considered: rapid guessing behaviour and cheating behaviour. Simulation results indicate that ability estimates could be improved after removing responses from aberrant behaviours identified by our approach. Two empirical examples were analysed to illustrate the application of the proposed sequential Bayesian changepoint detection procedure.

Estimating the Performance Loss Rate of Photovoltaic Systems Using Time Series Change Point Analysis

The accurate quantification of the performance loss rate of photovoltaic systems is critical for project economics. Following the current research activities in the photovoltaic performance and reliability field, this work presents a comparative assessment between common change point methods for performance loss rate estimation of fielded photovoltaic installations. An extensive testing campaign was thus performed to evaluate time series analysis approaches for performance loss rate evaluation of photovoltaic systems. Historical electrical data from eleven photovoltaic systems installed in Nicosia, Cyprus, and the locations’ meteorological measurements over a period of 8 years were used for this investigation. The application of change point detection algorithms on the constructed monthly photovoltaic performance ratio series revealed that the obtained trend might not always be linear. Specifically, thin film photovoltaic systems showed nonlinear behavior, while nonlinearities were also detected for some crystalline silicon photovoltaic systems. When applying several change point techniques, different numbers and locations of changes were detected, resulting in different performance loss rate values (varying by up to 0.85%/year even for the same number of change points). The results highlighted the importance of the application of nonlinear techniques and the need to extract a robust nonlinear model for detecting significant changes in time series data and estimating accurately the performance loss rate of photovoltaic installations.

Optimal Change-Point Analysis of Pavement Condition Data for Identification of Homogeneous Sections

This paper examined the applicability of the pruned exact linear time (PELT) algorithm for optimal change-point analysis to delineate pavement into homogeneous sections based on road condition. The primary objective of the study was to address some of the limitations associated with existing delineation approaches, such as the AASHTO cumulative difference approach (CDA) and the Bayesian binary segmentation method. The paper presents a mathematical framework for the optimal change-point analysis of pavement deflection data collected on a runway of an international airport. Through an analytical comparative study, the paper demonstrated how the proposed approach is better than existing delineation methods in terms of accuracy in identifying the change points, flexibility in the choice of the number of homogeneous sections, and computational time. The approach provides an opportunity for practitioners and road agencies to integrate their experience and knowledge of the road network into decision-making about the location of change points and their count without compromising computational accuracy. The proposed method was found to be robust because the solutions are independent of the parameters chosen for the analysis.

Autocorrelation and Parameter Estimation in a Bayesian Change Point Model

A piecewise function can sometimes provide the best fit to a time series. The breaks in this function are called change points, which represent the point at which the statistical properties of the model change. Often, the exact placement of the change points is unknown, so an efficient algorithm is required to combat the combinatorial explosion in the number of potential solutions to the multiple change point problem. Bayesian solutions to the multiple change point problem can provide uncertainty estimates on both the number and location of change points in a dataset, but there has not yet been a systematic study to determine how the choice of hyperparameters or the presence of autocorrelation affects the inference made by the model. Here, we propose Bayesian model averaging as a way to address the uncertainty in the choice of hyperparameters and show how this approach highlights the most probable solution to the problem. Autocorrelation is addressed through a pre-whitening technique, which is shown to eliminate spurious change points that emerge due to a red noise process. However, pre-whitening a dataset tends to make true change points harder to detect. After an extensive simulation study, the model is applied to two climate applications: the Pacific Decadal Oscillation and a global surface temperature anomalies dataset.

Homogeneity tests of covariance for high-dimensional functional data with applications to event segmentation.

We consider inference problems for high-dimensional (HD) functional data with a dense number of T repeated measurements taken for a large number of p variables from a small number of n experimental units. The spatial and temporal dependence, high dimensionality, and dense number of repeated measurements pose theoretical and computational challenges. This paper has two aims; our first aim is to solve the theoretical and computational challenges in testing equivalence among covariance matrices from HD functional data. The second aim is to provide computationally efficient and tuning-free tools with guaranteed stochastic error control. The weak convergence of the stochastic process formed by the test statistics is established under the "large p, large T, and small n" setting. If the null is rejected, we further show that the locations of the change points can be estimated consistently. The estimator's rate of convergence is shown to depend on the data dimension, sample size, number of repeated measurements, and signal-to-noise ratio. We also show that our proposed computation algorithms can significantly reduce the computation time and are applicable to real-world data with a large number of HD-repeated measurements (e.g., functional magnetic resonance imaging (fMRI) data). Simulation results demonstrate both the finite sample performance and computational effectiveness of our proposed procedures. We observe that the empirical size of the test is well controlled at the nominal level, and the locations of multiple change points can be accurately identified. An application to fMRI data demonstrates that our proposed methods can identify event boundaries in the preface of the television series Sherlock. Code to implement the procedures is available in an R package named TechPhD.

Hawkes Processes With Stochastic Exogenous Effects for Continuous-Time Interaction Modelling.

Continuous-time interaction data is usually generated under time-evolving environment. Hawkes processes (HP) are commonly used mechanisms for the analysis of such data. However, typical model implementations (such as e.g., stochastic block models) assume that the exogenous (background) interaction rate is constant, and so they are limited in their ability to adequately describe any complex time-evolution in the background rate of a process. In this paper, we introduce a stochastic exogenous rate Hawkes process (SE-HP) which is able to learn time variations in the exogenous rate. The model affiliates each node with a piecewise-constant membership distribution with an unknown number of changepoint locations, and allows these distributions to be related to the membership distributions of interacting nodes. The time-varying background rate function is derived through combinations of these membership functions. We introduce a stochastic gradient MCMC algorithm for efficient, scalable inference. The performance of the SE-HP is explored on real world, continuous-time interaction datasets, where we demonstrate that the SE-HP strongly outperforms comparable state-of-the-art methods.

A Geostatistical Framework Predicting Zooplankton Abundance in a Large River: Management Implications towards Potamoplankton Sustainability.

The zooplankton community is a widely used bioindicator for the biological assessment of riverine aquatic ecosystems. Phyto-zooplankton interaction and spatially varying river environment parameters perceivably govern their spatial distribution in a large river. This invites the challenge of predicting zooplankton abundance along the river channel. The present article has proposed a geostatistical framework to predict zooplankton abundance along the river course while decoupling phyto-zooplankton relationship from spatial dependency. The strength of secondary data on the river Narmada-a large tropical river in India-has been utilised to accomplish the goal. The nonlinear logistic regression kriging has been found to be the most effective framework. The phyto-zooplankton relationship captured 66% of zooplankton variability, having moderate (37%) residual spatial dependence. The results have shown longitudinally fluctuating spatial variability, which supports the river serial discontinuity concept. The proposed framework has generated smooth zooplankton abundance and sustainability predictive maps that have allowed detection of the change point locations of zooplankton abundance. The map has precisely identified the most productive zone of zooplankton sustainability. The study also has appraised obtaining approximate data in the areas where sampling is infeasible, which will be helpful for location-specific management strategies on a lower spatial scale.

Multiscale change point detection via gradual bandwidth adjustment in moving sum processes

A method for the detection of changes in the expectation in univariate sequences is provided. Moving sum processes (MOSUM) are studied. These rely on the selection of a tuning bandwidth. Here, a framework to overcome bandwidth selection is presented – the bandwidth adjusts gradually. For that, MOSUM are made dependent on both time and the bandwidth: the domain becomes a triangle. On the triangle, paths are constructed which systematically lead to change points. An algorithm is provided that estimates change points by subsequent consideration of paths. Strong consistency for the number and location of change points is shown. Simulation studies corroborate estimation precision and reveal competitiveness with state of the art change point detection methods. A companion R-package mscp is made available on CRAN.

Estimation of high-dimensional change-points under a group sparsity structure

Change-points are a routine feature of ‘big data’ observed in the form of high-dimensional data streams. In many such data streams, the component series possess group structures and it is natural to assume that changes only occur in a small number of all groups. We propose a new change point procedure, called groupInspect, that exploits the group sparsity structure to estimate a projection direction so as to aggregate information across the component series to successfully estimate the change-point in the mean structure of the series. We prove that the estimated projection direction is minimax optimal, up to logarithmic factors, when all group sizes are of comparable order. Moreover, our theory provide strong guarantees on the rate of convergence of the change-point location estimator. Numerical studies demonstrates the competitive performance of groupInspect in a wide range of settings and a real data example confirms the practical usefulness of our procedure.

A Univariate Extreme Value Analysis and Change Point Detection of Monthly Discharge in Kali Kupang, Central Java, Indonesia

Kali Kupang plays an important role in the life of the people of Pekalongan and its surrounding areas. However, until recently, not many hydrological studies have been carried out in this area. This study presents how Extreme Value Analysis (EVA) can predict future extreme hydrological events and how a dynamic-programming-based change point detection algorithm can detect the abrupt transition in discharge events variability. Using the annual block maxima, we can predict the upper extreme discharge probability from the generalized extreme value distribution (GEVD) that best fits the data by using the Markov Chain Monte Carlo (MCMC) algorithm as a distribution fitting method. Metropolis-Hasting (MH) algorithm with 500 walkers and 2,500 samples for each walker is used to generate random samples from the prior distribution. As a result, this discharge data can be categorized as a Gumbel distribution (  = 6.818,  = 3.456, and  = 0). The recurrence intervals (RI) for this discharge data can be calculated through this distribution. The changepoint location of the annual standard deviation of this discharge data in the mid-1990s is detected by using the pruned exact linear time (PELT) algorithm. Despite some shortcomings, this study can pave the way for using data-driven algorithms, along with more traditional numerical and descriptive approaches, to analyze hydrological time-series data in Indonesia. This is crucial, considering an increasing number of hydro climatological disasters in the future as a consequence of global climate change.

Structural Change Analysis of Active Cryptocurrency Market

Motivated by the large frequent price fluctuation and excessive volatility observed in the cryptocurrency market, this study adopts Bai and Perron’s structural change model by incorporating the trading volume and autoregressive variables to examine the number and location of change points in daily closing price, return and volatility proxied by the squared return of Cryptocurrency Index, Cryptocurrency Index 30, and the top 10 cryptocurrencies ranked according to market capitalisation. Results show that the structural changes occur very frequently for the price series, followed by squared return and return series which were consistently observed between December 2017 to April 2018. In addition, the results also reveal that the two cryptocurrency indices may not be beneficial as an indicator to reflect the whole cryptocurrency market for the entire studied period as these two indices do not display consistent structural change in contrast to the top 10 cryptocurrencies that might have significant implications for modelling the cryptocurrency data.

Regional mutational signature activities in cancer genomes.

Cancer genomes harbor a catalog of somatic mutations. The type and genomic context of these mutations depend on their causes and allow their attribution to particular mutational signatures. Previous work has shown that mutational signature activities change over the course of tumor development, but investigations of genomic region variability in mutational signatures have been limited. Here, we expand upon this work by constructing regional profiles of mutational signature activities over 2,203 whole genomes across 25 tumor types, using data aggregated by the Pan-Cancer Analysis of Whole Genomes (PCAWG) consortium. We present GenomeTrackSig as an extension to the TrackSig R package to construct regional signature profiles using optimal segmentation and the expectation-maximization (EM) algorithm. We find that 426 genomes from 20 tumor types display at least one change in mutational signature activities (changepoint), and 306 genomes contain at least one of 54 recurrent changepoints shared by seven or more genomes of the same tumor type. Five recurrent changepoint locations are shared by multiple tumor types. Within these regions, the particular signature changes are often consistent across samples of the same type and some, but not all, are characterized by signatures associated with subclonal expansion. The changepoints we found cannot strictly be explained by gene density, mutation density, or cell-of-origin chromatin state. We hypothesize that they reflect a confluence of factors including evolutionary timing of mutational processes, regional differences in somatic mutation rate, large-scale changes in chromatin state that may be tissue type-specific, and changes in chromatin accessibility during subclonal expansion. These results provide insight into the regional effects of DNA damage and repair processes, and may help us localize genomic and epigenomic changes that occur during cancer development.

Bayesian SIR model with change points with application to the Omicron wave in Singapore

The Omicron variant has led to a new wave of the COVID-19 pandemic worldwide, with unprecedented numbers of daily confirmed new cases in many countries and areas. To analyze the impact of society or policy changes on the development of the Omicron wave, the stochastic susceptible-infected-removed (SIR) model with change points is proposed to accommodate the situations where the transmission rate and the removal rate may vary significantly at change points. Bayesian inference based on a Markov chain Monte Carlo algorithm is developed to estimate both the locations of change points as well as the transmission rate and removal rate within each stage. Experiments on simulated data reveal the effectiveness of the proposed method, and several stages are detected in analyzing the Omicron wave data in Singapore.

Multi-threshold proportional hazards model and subgroup identification.

We propose a novel two-stage procedure for change point detection and parameter estimation in a multi-threshold proportional hazards model. In the first stage, we estimate the number of thresholds by formulating the threshold detection problem as a variable selection problem and applying the penalized partial likelihood approach. In the second stage, the change point locations are refined by a grid search and the standard inference for segment regression can then follow. The proposed model and estimation procedure could lend support to subgroup identification and personalized treatment recommendation in medical research. We establish the consistency of the threshold estimators and regression coefficient estimators under technical conditions. The finite sample performance of the method is demonstrated via simulation studies and two cancer data examples.

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.

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.

The importance of ocular artifact removal in single-trial ERP analysis: The case of the N250 in face learning

ObjectiveSingle-trial event-related potentials (ERPs) offer fine-grained information about the trajectories of the neurocognitive processes but are highly sensitive to any artifacts in the EEG signal. The primary aim of this study was to assess the impact of ocular artifact removal on the single-trial N250 ERP analysis of face learning in individual participants. MethodsWe present a detailed description of our research-grade EEG hardware setup and a highly reproducible code (https://osf.io/aqhmn/) for generating time series of single-trial N250 ERP amplitudes and precise identification of a changepoint between face memory trace acquisition and maintenance. Ocular artifacts were removed using a new semi-automatic approach with only one hyperparameter based on the correlation between EEG components from independent component analysis (ICA) and the EOG signal. ResultsResults from the simulation study showed that our ocular artifact filtration decreased the average RMSE by half and achieved the highest increase of SNR among all the compared methods. It decreased standard deviations and improved the fit of the broken-line regression models for all participants by 25% ± 17% (min. 2%, max. 63%). Conclusions and significanceOcular artifact filtration had a substantial positive impact on the regression modeling of single-trial ERP amplitudes. Lack of ocular artifact removal can drastically distort the conclusions about the face learning process from single-trial N250 ERP experiments for individual participants. The changepoint locations changed for 13 out of 15 participants. This is the first published analysis of time series of single-trial N250 ERP amplitudes in face learning.

High-dimensional Changepoint Estimation with Heterogeneous Missingness

AbstractWe propose a new method for changepoint estimation in partially observed, high-dimensional time series that undergo a simultaneous change in mean in a sparse subset of coordinates. Our first methodological contribution is to introduce a ‘MissCUSUM’ transformation (a generalisation of the popular cumulative sum statistics), that captures the interaction between the signal strength and the level of missingness in each coordinate. In order to borrow strength across the coordinates, we propose to project these MissCUSUM statistics along a direction found as the solution to a penalised optimisation problem tailored to the specific sparsity structure. The changepoint can then be estimated as the location of the peak of the absolute value of the projected univariate series. In a model that allows different missingness probabilities in different component series, we identify that the key interaction between the missingness and the signal is a weighted sum of squares of the signal change in each coordinate, with weights given by the observation probabilities. More specifically, we prove that the angle between the estimated and oracle projection directions, as well as the changepoint location error, are controlled with high probability by the sum of two terms, both involving this weighted sum of squares, and representing the error incurred due to noise and the error due to missingness respectively. A lower bound confirms that our changepoint estimator, which we call MissInspect, is optimal up to a logarithmic factor. The striking effectiveness of the MissInspect methodology is further demonstrated both on simulated data, and on an oceanographic data set covering the Neogene period.