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Relating and comparing methods for detecting changes in mean

STAT 2020年第1期9卷 1-11页

作者： Fearnhead, Paul Rigaill, Guillem Univ Lancaster Dept Math & Stat Lancaster LA1 4YF England Univ Evry Univ Paris Saclay CNRS INRAEInst Plant Sci Paris Saclay IPS2 F-91405 Orsay France Univ Paris CNRS Inst Plant Sci Paris Saclay IPS2 INRAE F-91405 Orsay France Univ Evry Univ Paris Saclay CNRS Lab Math & Modelisat Evry F-91037 Evry France

In recent years, there have been a large number of proposed approaches to detecting changes in mean. A natural question for an analyst is which method is most appropriate for their applications. Answering this question is difficult because current empirical studies often give conflicting conclusions. This paper aims to show the similarities and differences between different changepoint methods. We highlight that there are two aspects to estimating changepoints: estimating the number of changes and estimating their locations, and that comparisons should separately evaluate these two aspects. We perform an extensive comparison of different methods across a range of simulation scenarios and provide code and full results for an interested practitioner to extend this comparison to more methods or different scenarios.

关键词： binary segmentation breakpoints dynamic programming model error penalized likelihood structural breaks

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A MOSUM procedure for the estimation of multiple random change points

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BERNOULLI 2018年第1期24卷 526-564页

作者： Eichinger, Birte Kirch, Claudia Karlsruhe Inst Technol KIT Inst Stochast Kaiserstr 89 D-76133 Karlsruhe Germany Otto von Guericke Univ Inst Math Stochast Postfach 4120 D-39106 Magdeburg Germany

In this work, we investigate statistical properties of change point estimators based on moving sum statistics. We extend results for testing in a classical situation with multiple deterministic change points by allowing for random exogenous change points that arise in Hidden Markov or regime switching models among others. To this end, we consider a multiple mean change model with possible time series errors and prove that the number and location of change points are estimated consistently by this procedure. Additionally, we derive rates of convergence for the estimation of the location of the change points and show that these rates are strict by deriving the limit distribution of properly scaled estimators. Because the small sample behavior depends crucially on how the asymptotic (long-run) variance of the error sequence is estimated, we propose to use moving sum type estimators for the (long-run) variance and derive their asymptotic properties. While they do not estimate the variance consistently at every point in time, they can still be used to consistently estimate the number and location of the changes. In fact, this inconsistency can even lead to more precise estimators for the change points. Finally, some simulations illustrate the behavior of the estimators in small samples showing that its performance is very good compared to existing methods.

关键词： binary segmentation change point hidden Markov model moving sum statistics regime switching model

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Linear Time Dynamic Programming for Computing Breakpoints in the Regularization Path of Models Selected From a Finite Set

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JOURNAL OF COMPUTATIONAL AND GRAPHICAL STATISTICS 2022年第2期31卷 313-323页

作者： Vargovich, Joseph Hocking, Toby Dylan No Arizona Univ SICCS Machine Learning Res Lab Flagstaff AZ 86011 USA

Many learning algorithms are formulated in terms of finding model parameters which minimize a data-fitting loss function plus a regularizer. When the regularizer involves the l(0) pseudo-norm, the resulting regularization path consists of a finite set of models. The fastest existing algorithm for computing the breakpoints in the regularization path is quadratic in the number of models, so it scales poorly to high-dimensional problems. We provide new formal proofs that a dynamic programming algorithm can be used to compute the breakpoints in linear time. Our empirical results include analysis of the proposed algorithm in the context of various learning problems (regression, changepoint detection, clustering, and matrix factorization). We use a detailed analysis of changepoint detection problems to demonstrate the improved accuracy and speed of our approach relative to grid search and a previous quadratic time algorithm.

关键词： binary segmentation Changepoint detection Dynamic programming Model selection

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LIKELIHOOD RATIO TESTS FOR A CHANGE IN THE MULTIVARIATE NORMAL-MEAN

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JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION 1986年第393期81卷 199-204页

作者： SRIVASTAVA, MS WORSLEY, KJ MCGILL UNIV DEPT MATH & STATMONTREAL H3A 2K6QUEBECCANADA

A sequence of independent multivariate normal vectors with equal but possibly unknown variance matrices are hypothesized to have equal mean vectors, and we wish to test that the mean vectors have changed after an unknown point in the sequence. The likelihood ratio test is based on the maximum Hotelling T2 for the sequences before and after the change point. The main result is a conservative approximation for its null distribution based on an improved Bonferroni inequality. If the change is judged significant, then further changes are estimated by splitting the two subsequences formed by the first change point. The methods can also be used to test for a change in row probabilities of a contingency table, allowing for extramultinomial variation. The results are used to find changes in a set of geological data previously analyzed by Chernoff (1973) by the "faces" method and to find changes in the frequencies of pronouns in the plays of Shakespeare.

关键词： Change point binary segmentation Bonferroni inequality Extramultinomial variation

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Subgroup identification via homogeneity pursuit for dense longitudinal/spatial data

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STATISTICS IN MEDICINE 2019年第17期38卷 3256-3271页

作者： Li, Jialiang Yue, Mu Zhang, Wenyang Natl Univ Singapore Dept Stat & Appl Probabil Singapore Singapore Duke NUS Med Sch Singapore Singapore Singapore Eye Res Inst Singapore Singapore Univ Elect Sci & Technol China Sch Math Sci Chengdu 611731 Sichuan Peoples R China Univ York Dept Math York N Yorkshire England

In the clinical trial community, it is usually not easy to find a treatment that benefits all patients since the reaction to treatment may differ substantially across different patient subgroups. The heterogeneity of treatment effect plays an essential role in personalized medicine. To facilitate the development of tailored therapies and improve the treatment efficacy, it is important to identify subgroups that exhibit different treatment effects. We consider a very general framework for subgroup identification via the homogeneity pursuit methods usually employed in econometric time series analysis. The change point detection algorithm in our procedure is most suitable for analyzing dense longitudinal or spatial data which are quite common for biomedical studies these days. We demonstrate that our proposed method is fast and accurate through extensive numerical studies. In particular, our method is illustrated by analyzing a diffusion tensor imaging data set.

关键词： binary segmentation change point detection dense longitudinal data homogeneity pursuit personalized medicine treatment recommendation

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Unbalanced Haar technique for nonparametric function estimation

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JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION 2007年第480期102卷 1318-1327页

作者： Fryzlewicz, Piotr Univ Bristol Dept Math Bristol BS8 1TW Avon England

The discrete unbalanced Haar (UH) transform is a decomposition of one-dimensional data with respect to an orthonormal Haar-like basis where jumps in the basis vectors do not necessarily occur in the middle of their support. We introduce a multiscale procedure for estimation in Gaussian noise that consists of three steps: a UH transform, thresholding of the decomposition coefficients, and the inverse UH transform. We show that our estimator is mean squared consistent with near-optimal rates for a wide range of functions, uniformly over UH bases that are not "too unbalanced." A vital ingredient of our approach is basis selection. We choose each basis vector so that it best matches the data at a specific scale and location, where the latter parameters are determined by the "parent" basis vector. Our estimator is computable in O(n log n) operations. A simulation study demonstrates the good performance of our estimator compared with state-of-the-art competitors. We apply our method to the estimation of the mean intensity of the time series of earthquake counts occurring in northern California. We discuss extensions to image data and to smoother wavelets.

关键词： adaptive smooting binary segmentation CART matching pursuit piecewise constant estimators wavelets

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Tire Surface segmentation in Infrared Imaging with Convolutional Neural Networks and Transfer Learning

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PATTERN RECOGNITION AND IMAGE ANALYSIS 2021年第3期31卷 466-476页

作者： Nava, Rodrigo Fehr, Duc Petry, Frank Tamisier, Thomas Luxembourg Inst Sci & Technol LIST L-4362 Esch Sur Alzette Luxembourg Goodyear Innovat Ctr Luxembourg L-7750 Colmar Berg Luxembourg

It is crucial to analyze the tire under dynamic conditions to observe a performance close to realistic situations. Particularly, the temperature generated by the interaction of tire and pavement can provide useful information and understanding into how tire components can be optimized. However, in such a situation, data generation and measurement are challenging tasks. High-resolution thermal infrared imaging is a non-contact technology that transforms radiation patterns into a visible image and allows measuring the temperature changes on the surface of the tire. Therefore, the first step towards a systematic analysis of the performance of the tire is to segment the surface. To this end, we present an approach that combines traditional image processing methods with convolutional neural networks. We further investigate transfer learning techniques to improve the prediction of the proposed model on a different dataset. Our ultimate goal is to implement a robust network to segment a broad variety of tires. A segmentation accuracy >0.97 and a validation error <0.06 were achieved with transfer learning. The results have shown that our network can be extended to segment new data accurately.

关键词： binary segmentation convolutional neural networks inception tire segmentation thermal infrared imaging transfer learning U-Net

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Statistical inference for multiple change-point models

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SCANDINAVIAN JOURNAL OF STATISTICS 2020年第4期47卷 1149-1170页

作者： Wang, Wu He, Xuming Zhu, Zhongyi King Abdullah Univ Sci & Technol Stat Program Thuwal Saudi Arabia Univ Michigan Dept Stat Ann Arbor MI 48109 USA Fudan Univ Dept Stat 670 Guoshun Rd Shanghai Peoples R China

In this article, we propose a new technique for constructing confidence intervals for the mean of a noisy sequence with multiple change-points. We use the weighted bootstrap to generalize the bootstrap aggregating or bagging estimator. A standard deviation formula for the bagging estimator is introduced, based on which smoothed confidence intervals are constructed. To further improve the performance of the smoothed interval for weak signals, we suggest a strategy of adaptively choosing between the percentile intervals and the smoothed intervals. A new intensity plot is proposed to visualize the pattern of the change-points. We also propose a new change-point estimator based on the intensity plot, which has superior performance in comparison with the state-of-the-art segmentation methods. The finite sample performance of the confidence intervals and the change-point estimator are evaluated through Monte Carlo studies and illustrated with a real data example.

关键词： bagging estimator binary segmentation bootstrap copy number variation multiple change-points

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Testing for a change in mean after changepoint detection

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JOURNAL OF THE ROYAL STATISTICAL SOCIETY SERIES B-STATISTICAL METHODOLOGY 2022年第4期84卷 1082-1104页

作者： Jewell, Sean Fearnhead, Paul Witten, Daniela Univ Washington Dept Stat Seattle WA 98195 USA Univ Lancaster Dept Math & Stat Lancaster England Univ Washington Dept Biostat Seattle WA 98195 USA

While many methods are available to detect structural changes in a time series, few procedures are available to quantify the uncertainty of these estimates post-detection. In this work, we fill this gap by proposing a new framework to test the null hypothesis that there is no change in mean around an estimated changepoint. We further show that it is possible to efficiently carry out this framework in the case of changepoints estimated by binary segmentation and its variants, l0 segmentation, or the fused lasso. Our setup allows us to condition on much less information than existing approaches, which yields higher powered tests. We apply our proposals in a simulation study and on a dataset of chromosomal guanine-cytosine content. These approaches are freely available in the R package ChangepointInference at -inference/.

关键词： l0 optimization binary segmentation fused lasso selective inference

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Changepoint Detection in the Presence of Outliers

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JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION 2019年第525期114卷 169-183页

作者： Fearnhead, Paul Rigaill, Guillem Univ Lancaster Dept Math & Stat Lancaster LA1 4YF England Univ Paris Diderot Sorbonne Paris Cite Univ EvryCNRSUMR 9213UMR1403 Univ Paris SudInst Plant Sci Paris SaclayINRA Paris France Univ Evry Val dEssonne Lab Math Modelisat Evry LaMME CNRS UMR 8071ENSIIEUSCINRA Paris France

Many traditional methods for identifying changepoints can struggle in the presence of outliers, or when the noise is heavy-tailed. Often they will infer additional changepoints to fit the outliers. To overcome this problem, data often needs to be preprocessed to remove outliers, though this is difficult for applications where the data needs to be analyzed online. We present an approach to changepoint detection that is robust to the presence of outliers. The idea is to adapt existing penalized cost approaches for detecting changes so that they use loss functions that are less sensitive to outliers. We argue that loss functions that are bounded, such as the classical biweight loss, are particularly suitableas we show that only bounded loss functions are robust to arbitrarily extreme outliers. We present an efficient dynamic programming algorithm that can find the optimal segmentation under our penalized cost criteria. Importantly, this algorithm can be used in settings where the data needs to be analyzed online. We show that we can consistently estimate the number of changepoints, and accurately estimate their locations, using the biweight loss function. We demonstrate the usefulness of our approach for applications such as analyzing well-log data, detecting copy number variation, and detecting tampering of wireless devices. Supplementary materials for this article are available online.

关键词： binary segmentation Biweight loss Cusum M-estimation Penalized likelihood Robust statistics

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