Localising change points in piecewise polynomials of general degrees

Yu, Yijun; Chatterjee, Sabyasachi

doi:10.1214/21-ejs1963

Cited by 9 publications

(3 citation statements)

References 42 publications

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“…Changepoint detection . In modeling the evolution of dynamic systems, an important perspective is to detect structural changes (Padilla et al, 2022; Wang et al, 2021; Yi et al, 2022). Traditional changepoint detection methods usually focus on changes in particular features of the underlying population; and in the analysis of network growth, reliable detection methods for changes in network features or sudden shifts are also important to understand the distributional structure of the evolving network.…”

Section: Discussionmentioning

confidence: 99%

Recent advances on mechanisms of network generation: Community, exchangeability, and scale‐free properties

Li,

Hou,

Wang

2024

WIREs Computational Stats

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The mechanisms of network generation have undergone extensive analysis and found broad applications in various real‐world scenarios. Among the fruitful literature on network models, numerous studies seek to explore and interpret fundamental graph structure properties, including the clustering effect, exchangeability, and scale‐free properties. In this paper, we present a comprehensive review of the statistical modeling methods for the mechanisms of network generation. We specifically focus on three representative classes of models, namely the stochastic block models, the exchangeable network models, and the preferential attachment models. For each model type, our approach begins by reviewing existing methods and model setups, followed by an exploration of the core modeling principles behind them. We also summarize relevant statistical inference techniques and provide a unified understanding of theoretical analyses. Furthermore, we emphasize several challenges and open problems that could shed light on future research. We conclude this review with the identification of some possible directions for future study.This article is categorized under: Statistical and Graphical Methods of Data Analysis > Modeling Methods and Algorithms Algorithms and Computational Methods > Networks and Security

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Section: Discussionmentioning

confidence: 99%

Recent advances on mechanisms of network generation: Community, exchangeability, and scale‐free properties

Li,

Hou,

Wang

2024

WIREs Computational Stats

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“…In additiona to the applications considered in Section 3, the general framework can be readily applied to more complicated cases, for example, the signal within the segments is non-linear [38], structure changes is in the moments or quantiles [14,1], and other structure changes such as and autocovariance in time series. Moreover, as mentioned earlier the gaussianity condition on the noise can be relaxed as well [13].…”

Section: Discussionmentioning

confidence: 99%

Consistency of a range of penalised cost approaches for detecting multiple changepoints

Zheng¹,

Eckley²,

Fearnhead³

2022

Electron. J. Statist.

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A common approach to detect multiple changepoints is to minimise a measure of data fit plus a penalty that is linear in the number of changepoints. This paper shows that the general finite sample behaviour of such a method can be related to its behaviour when analysing data with either none or one changepoint. This property results in simpler conditions for verifying whether the method will consistently estimate the number and locations of the changepoints. We apply and demonstrate the usefulness of these simple conditions for a range of changepoint problems. Our new results include a weaker requirement on the choice of penalty to have consistency in a change-in-slope model; and the first results for the accuracy of recently-proposed methods for detecting spikes.

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“…A related problem to detecting changes-in-slope is that of fitting piecewise polynomial functions. Yu, Chatterjee, and Xu (2022) present a method for detecting such changes by minimizing a measure of fit to the data with an L 0 penalty, which is the same as used by CPOP. However they do not require the fitted polynomial functions to be continuous at the change-points, which means that it is simple to minimize this criteria using standard dynamic For trend filtering we chose the L 1 penalty value based on crossvalidation (middle left) or so that it obtained the correct number of changes (middle right).…”

Section: Introductionmentioning

confidence: 99%

cpop: Detecting Changes in Piecewise-Linear Signals

Fearnhead,

Grose

2024

J. Stat. Soft.

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Changepoint detection is an important problem with a wide range of applications. There are many different types of changes that one may wish to detect, and a wide range of algorithms and software for detecting them. However there are relatively few approaches for detecting changes-in-slope in the mean of a signal plus noise model. We describe the R package cpop, available on the Comprehensive R Archive Network (CRAN). This package implements CPOP, a dynamic programming algorithm, to find the optimal set of changes that minimizes an L 0 penalized cost, with the cost being a weighted residual sum of squares. The package has extended the CPOP algorithm so it can analyse data that is unevenly spaced, allow for heterogeneous noise variance, and allows for a grid of potential change locations to be different from the locations of the data points. There is also an implementation that uses the CROPS algorithm to detect all segmentations that are optimal as you vary the L 0 penalty for adding a change across a continuous range of values.

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Localising change points in piecewise polynomials of general degrees

Cited by 9 publications

References 42 publications

Recent advances on mechanisms of network generation: Community, exchangeability, and scale‐free properties

Recent advances on mechanisms of network generation: Community, exchangeability, and scale‐free properties

Consistency of a range of penalised cost approaches for detecting multiple changepoints

cpop: Detecting Changes in Piecewise-Linear Signals

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