Using penalized contrasts for the change-point problem

Lavielle, Marc

doi:10.1016/j.sigpro.2005.01.012

Cited by 513 publications

(445 citation statements)

References 8 publications

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“…This can be seen as a change-point detection [9] problem: Given y(t), a noisy observation of a piecewise regular signal x(t), we want to detect the abrupt changes and estimate their locations. The problem is widely studied in the literature where the statistical approach naturally takes the dominant role (see [9], [10] and their references). Here, we apply a purely algebraic approach (see [6], [11] and [12] for the details).…”

Section: Description Of Our Approachmentioning

confidence: 99%

An Algebraic Method for Eye Blink Artifacts Detection in Single Channel EEG Recordings

et al. 2010

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Section: Description Of Our Approachmentioning

confidence: 99%

An Algebraic Method for Eye Blink Artifacts Detection in Single Channel EEG Recordings

et al. 2010

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“…We use CROPS with ED-PELT with ξ min = 25, ξ max = 200 and K = 4 log(n) (the results are similar for different K ). In order to choose the best segmentation we use the approach suggested by Lavielle (2005). This involves plotting the segmentation cost against the number of changepoints and then looking for an "elbow" in the plot.…”

Section: Nonparametric Changepoint Detectionmentioning

confidence: 99%

“…For example a common approach is to introduce a model for the data within a segment, use minus the maximum of the resulting log-likelihood to define a cost for a segment, and then define a cost of a segmentation as the sum of the costs for each of its segments. See for example Yao (1988), Lavielle (2005), Killick et al (2012) and Davis et al (2006). Finally, the segmentation of the data is obtained as the one that minimises a penalised version of this cost (see also Frick et al 2014, for an extension of these approaches).…”

Section: Introductionmentioning

confidence: 99%

A computationally efficient nonparametric approach for changepoint detection

2016

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In this paper we build on an approach proposed by for nonparametric changepoint detection. This approach defines the best segmentation for a data set as the one which minimises a penalised cost function, with the cost function defined in term of minus a non-parametric loglikelihood for data within each segment. Minimising this cost function is possible using dynamic programming, but their algorithm had a computational cost that is cubic in the length of the data set. To speed up computation, resorted to a screening procedure which means that the estimated segmentation is no longer guaranteed to be the global minimum of the cost function. We show that the screening procedure adversely affects the accuracy of the changepoint detection method, and show how a faster dynamic programming algorithm, pruned exact linear time (PELT) (Killick et al. 2012), can be used to find the optimal segmentation with a computational cost that can be close to linear in the amount of data. PELT requires a penalty to avoid under/over-fitting the model which can have a detrimental effect on the quality of the detected changepoints. To overcome this issue we use a relatively new method, changepoints over a range of penalties (Haynes et al. 2016), which finds all of the optimal segmentations for multiple penalty values over a continuous range. We apply our method to detect changes in heart-rate during physical activity. Electronic supplementary materialThe online version of this article

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“…An alternative frequentist approach is the binary segmentation procedure that tests recursively the presence of a change-point until no segments have any more change-points (Olshen and Venlatraman 2004). A variety of Penalized Maximum Likelihood estimators have also been used to estimate and test structural breaks, such as the penalized contrast estimator (Lavielle 2005), the minimum description length principle (Davis, Lee, and Rodriguez-Yam 2006), and many others (e.g., Siegmund 2004;Zhang and Siegmund 2007). There is a large Bayesian literature on multiple change-point models (e.g., Carlin, Gelfand, and Smith 1992;Barry and Hartigan 1993;Chib 1996Chib , 1998Hawkins 2001;Minin et al 2005).…”

Section: A Multiple Change-point Modelmentioning

confidence: 99%

Endogenous Jurisprudential Regimes

Pang

Friedman²,

Martin³

et al. 2012

Polit. anal.

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Edited by R. Michael AlvarezJurisprudential regime theory is a legal explanation of decision-making on the U.S. Supreme Court that asserts that a key precedent in an area of law fundamentally restructures the relationship between case characteristics and the outcomes of future cases. In this article, we offer a multivariate multiple change-point probit model that can be used to endogenously test for the existence of jurisprudential regimes. Unlike the previously employed methods, our model does so by estimating the locations of many possible changepoints along with structural parameters. We estimate the model using Markov chain Monte Carlo methods, and use Bayesian model comparison to determine the number of change-points. Our findings are consistent with jurisprudential regimes in the Establishment Clause and administrative law contexts. We find little support for hypothesized regimes in the areas of free speech and search-and-seizure. The Bayesian multivariate change-point model we propose has broad potential applications to studying structural breaks in either regular or irregular time-series data about political institutions or processes.1 Modeling Decision-Making on the U.S. Supreme Court Supreme Court decisions do two things: they award a judgment, and they provide a rationale for that judgment in the form of a written opinion. The judgment of the case determines who wins and who loses in the legal dispute, and the terms of the victory or defeat. Opinions are important because they provide justifications for the judgment. Those who subscribe to the attitudinal model of judging (Segal and Spaeth 2002)-which asserts that the decisions the Justices reach are due solely to politics-argue that opinions are nothing more than disingenuous post hoc rationalizations of behavior that merely serve to cover up nothing more than unfettered politics.Authors' note: The authors thank Bert Kritzer, Mark Richards, and Jeff Segal for sharing replication data; Jude Hayes and Robert Walker, along with seminar participants at SLAMM 2010, NYU, and USC for helpful comments; Katie Schon, Jee Seon Jeon, and Rachael Hinkle for their research assistance; and the Filomen D'Agostino and Max E. Greenberg Research Fund at NYU School of Law, the Center for Empirical Research in the Law at Washington University, the Wang Xuelian Fund at Tsinghua University, and the National Science Foundation for supporting our research. The editor, R. Michael Alvarez, and two anonymous referees made suggestions that improved the article significantly. For replication data and code, see Pang et al. (2012). Supplementary materials for this article are available on the Political Analysis Web site.Political Analysis (2012) On the other hand, from a legal standpoint, it is hard to believe that opinions are inconsequential (Friedman 2006). To be sure, opinions are justifications, but they also provide legal rules that govern in future disputes. In our common law system, lower court judges rely on the collection of these rules-called precedents-when deciding s...

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Using penalized contrasts for the change-point problem

Cited by 513 publications

References 8 publications

An Algebraic Method for Eye Blink Artifacts Detection in Single Channel EEG Recordings

An Algebraic Method for Eye Blink Artifacts Detection in Single Channel EEG Recordings

A computationally efficient nonparametric approach for changepoint detection

Endogenous Jurisprudential Regimes

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