A Kernel Multiple Change-point Algorithm via Model Selection

Arlot, Sylvain; Celisse, Alain; Harchaoui, Zaid

doi:10.48550/arxiv.1202.3878

Cited by 8 publications

(29 citation statements)

References 42 publications

(90 reference statements)

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“…From now, we will assume that k is characteristic. Note that there are many applications of the kernel mean embedding and MMD in statistics such as two-sample testing [Gretton et al, 2012], change-point detection [Arlot et al, 2012], detection , we refer the reader to for a thorough introduction to the applications of kernels and MMD to computational biology .…”

Section: Maximum Mean Discrepancymentioning

confidence: 99%

Finite sample properties of parametric MMD estimation: robustness to misspecification and dependence

Chérief-Abdellatif,

Alquier

2019

Preprint

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Many works in statistics aim at designing a universal estimation procedure. This question is of major interest, in particular because it leads to robust estimators, a very hot topic in statistics and machine learning. In this paper, we tackle the problem of universal estimation using a minimum distance estimator presented in [Briol et al., 2019] based on the Maximum Mean Discrepancy. We show that the estimator is robust to both dependence and to the presence of outliers in the dataset. We also highlight the connections that may exist with minimum distance estimators using L2-distance. Finally, we provide a theoretical study of the stochastic gradient descent algorithm used to compute the estimator, and we support our findings with numerical simulations.

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Section: Maximum Mean Discrepancymentioning

confidence: 99%

Finite sample properties of parametric MMD estimation: robustness to misspecification and dependence

Chérief-Abdellatif,

Alquier

2019

Preprint

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“…For line (46) and line (47), from Proposition 3 of Arlot et al (2012), we have for any θ > 0 and x > 0, with probability at least 1…”

Section: B2 Some Useful Resultsmentioning

confidence: 99%

“…Utilizing Proposition 4 in Arlot et al (2012) and the fact that 0 < v 0 , v 1 ≤ M 2 , for any x > 0, when n is sufficiently large, with probability at least 1 − 16e −x , we have:…”

Section: B52 For Smentioning

confidence: 99%

Weighted-Graph-Based Change Point Detection

Nie,

Nicolae

2021

Preprint

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We consider the detection and localization of change points in the distribution of an offline sequence of observations. Based on a nonparametric framework that uses a similarity graph among observations, we propose new test statistics when at most one change point occurs and generalize them to multiple change points settings. The proposed statistics leverage edge weight information in the graphs, exhibiting substantial improvements in testing power and localization accuracy in simulations. We derive the null limiting distribution, provide accurate analytic approximations to control type I error, and establish theoretical guarantees on the power consistency under contiguous alternatives for the one change point setting, as well as the minimax localization rate. In the multiple change points setting, the asymptotic correctness of the number and location of change points are also guaranteed. The methods are illustrated on the MIT proximity network data.

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“…We consider here a more general setting where θ * t is piecewise constant and the distribution of Y t |F t−1 is unknown. 1 Supported by the Institute for advanced studies -IAS (Université de Cergy-Pontoise, France), the MME-DII center of excellence (ANR-11-LABEX-0023-01) and by the CEA-MITIC (Université Gaston Berger, Sénégal) 2 Developed within the ANR BREAKRISK : ANR-17-CE26-0001-01…”

Section: Introductionmentioning

confidence: 99%

“…This question is tacked by model selection approach. Numerous works have been devoted to this issue; see among others, Lebarbier (2005), Arlot and Massart (2009), Lebarbier (2014 and, Arlot and Celisse (2016).…”

Section: Introductionmentioning

confidence: 99%

Piecewise autoregression for general integer-valued time series

Diop¹,

Kengne²

2019

Preprint

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This paper proposes a piecewise autoregression for general integer-valued time series. The conditional mean of the process depends on a parameter which is piecewise constant over time. We derive an inference procedure based on a penalized contrast that is constructed from the Poisson quasi-maximum likelihood of the model. The consistency of the proposed estimator is established. From practical applications, we derive a data-driven procedure based on the slope heuristic to calibrate the penalty term of the contrast; and the implementation is carried out through the dynamic programming algorithm, which leads to a procedure of O(n 2 ) time complexity. Some simulation results are provided, as well as the applications to the US recession data and the number of trades in the stock of Technofirst.

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A Kernel Multiple Change-point Algorithm via Model Selection

Cited by 8 publications

References 42 publications

Finite sample properties of parametric MMD estimation: robustness to misspecification and dependence

Finite sample properties of parametric MMD estimation: robustness to misspecification and dependence

Weighted-Graph-Based Change Point Detection

Piecewise autoregression for general integer-valued time series

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