Multiple changepoint detection with partial information on changepoint times

Li, Yingbo; Lund, Robert; Hewaarachchi, A. P.

doi:10.1214/19-ejs1568

Cited by 8 publications

(13 citation statements)

References 57 publications

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“…A better penalty for this problem, and one that accounts for the location times of the changepoints, is the minimum description length (MDL) penalty of form

P (m; τ_{1}, …, τ_{m}; X) = \ln (m + 1) + \frac{1}{2} \sum_{r = 2}^{m + 1} \ln (τ_{r} - τ_{r - 1}) + \sum_{r = 2}^{m} \ln (τ_{r}) + \ln (N + 1)

if m ≥ 1 and zero if m =0. This penalty will be used here because of its superior performance in changepoint simulation studies (Li et al, ).…”

Section: Methodsmentioning

confidence: 99%

“…Our GA optimizes a minimum descriptive length (MDL) penalized likelihood. An MDL penalty, viewed akin to AICC and BIC penalties, is a penalty specifically tailored to the changepoint problem stemming from information criterion (Li, Lund, & Hewaarachchi, ). The MDL penalty is not proportional to the number of changepoints, but rather depends on the position of the individual changepoints: Changepoints occurring close together are penalized more heavily than sparsely occurring changepoints.…”

Section: Introductionmentioning

confidence: 99%

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Trend assessment for daily snow depths with changepoint considerations

et al. 2019

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This paper develops methods to estimate a long‐term trend in a daily snow depth record. The methods use a storage equation model for the daily snow depths that allows for seasonality, support set features (snow depths cannot be negative), correlation, and mean level shift changepoint features. Changepoints can occur in snow processes whenever observing stations move or station instrumentation is changed; they are critical features to consider when estimating a long‐term trend. A likelihood objective function is developed for the storage model and is used to estimate model parameters. Genetic algorithms are used to optimize a minimum descriptive length model selection criterion that estimates the changepoint numbers and locations. The methods are applied in the analysis of a daily series recorded near Warm Lake, Idaho, from 1948 to 2009.

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“…A better penalty for this problem, and one that accounts for the location times of the changepoints, is the minimum description length (MDL) penalty of form

P (m; τ_{1}, …, τ_{m}; X) = \ln (m + 1) + \frac{1}{2} \sum_{r = 2}^{m + 1} \ln (τ_{r} - τ_{r - 1}) + \sum_{r = 2}^{m} \ln (τ_{r}) + \ln (N + 1)

if m ≥ 1 and zero if m =0. This penalty will be used here because of its superior performance in changepoint simulation studies (Li et al, ).…”

Section: Methodsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Trend assessment for daily snow depths with changepoint considerations

et al. 2019

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“…Other available approaches use the principle of dynamic programming (see Antoch & Jarušková, ; Zeileis, Kleiber, Krämer, & Hornik, , and the references therein) and genetic algorithms (e.g., S. Li & Lund, ) to find a solution optimizing some likelihood function, which is usually the residual sum of squares, AIC, or BIC. Y. Li and Lund () and Y. Li, Lund, and Hewaarachchi () use Bayesian techniques to account for partial information about change points documented in metadata. A separate group of testing approaches that often do not require to set the upper limit m for the number of change points are developed for monitoring tasks (e.g., see Aue et al, ; Eichinger & Kirch, ; Horváth et al, ).…”

Section: Methodsmentioning

confidence: 99%

A data‐driven approach to detecting change points in linear regression models

2019

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Change points appear in various types of environmental data—from univariate time series to multivariate data structures—and need to be accounted for in proper analysis and inference. The analysis of change points is challenging when no exact information about their number and locations is available, and statistical tests developed under such conditions often have low power identifying the change points. This paper provides a powerful, data‐driven procedure for detecting at‐most‐m change points in linear regression models by adapting a sieve bootstrap approach for a modified cumulative sum statistic. The new procedure does not assume a particular dependence structure nor a particular distribution of regression residuals. It employs a data‐driven selection of the order of an autoregressive model and a robust estimation of the model coefficients. Our simulation studies show a competitive performance of the new bootstrap‐based procedure compared with its asymptotic counterpart. We apply the new testing procedure to address an important environmental problem in Chesapeake Bay—severe oxygen depletion—and detect two change points in the relationship between the volume of low‐oxygen waters and nutrient inputs to the bay during 1985–2017.

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“…Our goal is to select the most likely model given the observed data, i.e., to perform model selection. e objective function for the model selection will be derived based on the Bayesian Minimum Description Length (BMDL) framework [2]. For each candidate model, we compute its BMDL score; and among all models we visit, the one with the smallest BMDL score is the most optimal.…”

Section: Multiple Changepoint Con Gurationsmentioning

confidence: 99%

“…In this paper, we introduce a novel model-based changepoint detection approach, which is exible, explainable, easy to automate, and most importantly, e ective in reducing false positives. We follow the Bayesian Minimum Description Length (BMDL) framework in Li et al [2], and extend the method there to handle more exible data monitoring tasks. Our method automatically detects not only the optimal combinations of changepoint locations in the past, but also whether the time series data has seasonality and/or autocorrelation.…”

Section: Introductionmentioning

confidence: 99%

Automating Data Monitoring: Detecting Structural Breaks in Time Series Data Using Bayesian Minimum Description Length

Li,

Cezeaux,

2019

Preprint

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In modern business modeling and analytics, data monitoring plays a critical role. Nowadays, sophisticated models o en rely on hundreds or even thousands of input variables. Over time, structural changes such as abrupt level shi s or trend slope changes may occur among some of these variables, likely due to changes in economy or government policies. As a part of data monitoring, it is important to identify these changepoints, in terms of which variables exhibit such changes, and what time locations do the changepoints occur. Being alerted about the changepoints can help modelers decide if models need modi cation or rebuilds, while ignoring them may increase risks of model degrading.Simple process control rules o en ag too many false alarms because regular seasonal uctuations or steady upward or downward trends usually trigger alerts. To reduce potential false alarms, we create a novel statistical method based on the Bayesian Minimum Description Length (BMDL) framework to perform multiple changepoint detection. Our method is capable of detecting all structural breaks occurred in the past, and automatically handling data with or without seasonality and/or autocorrelation. It is implemented with computation algorithms such as Markov chain Monte Carlo (MCMC), and can be applied to all variables in parallel.As an explainable anomaly detection tool, our changepoint detection method not only triggers alerts, but provides useful information about the structural breaks, such as the times of changepoints, and estimation of mean levels and linear slopes before and a er the changepoints. is makes future business analysis and evaluation on the structural breaks easier.

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Multiple changepoint detection with partial information on changepoint times

Cited by 8 publications

References 57 publications

Trend assessment for daily snow depths with changepoint considerations

Trend assessment for daily snow depths with changepoint considerations

A data‐driven approach to detecting change points in linear regression models

Automating Data Monitoring: Detecting Structural Breaks in Time Series Data Using Bayesian Minimum Description Length

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