Change Point Estimation in High Dimensional Markov Random-Field Models

Roy, Sandipan; Atchadé, Yves F.; Michailidis, George

doi:10.1111/rssb.12205

Cited by 49 publications

(60 citation statements)

References 26 publications

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“…Chen introduced a nonparametric method for detecting change via a k nearest neighbor approach. Roy et al considered change point analysis in high‐dimensional Markov fields, and Keshavarz et al extended this work to Gaussian graphical models.…”

Section: Related Workmentioning

confidence: 99%

Modeling and detecting change in temporal networks via the degree corrected stochastic block model

Wilson

Stevens

Woodall

2019

Quality & Reliability Eng

109

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In many applications, it is of interest to identify anomalous behavior within a dynamic interacting system. Such anomalous interactions are reflected by structural changes in the network representation of the system. We propose and investigate the use of the degree corrected stochastic block model (DCSBM) to model and monitor dynamic networks that undergo a significant structural change. We apply statistical process monitoring techniques to the estimated parameters of the DCSBM to identify significant structural changes in the network. We apply our surveillance strategy to a dynamic US Senate covoting network. We detect significant changes in the political network that reflect both times of cohesion and times of polarization among Republican and Democratic party members. Our analysis demonstrates that the DCSBM monitoring procedure effectively detects local and global structural changes in complex networks, providing useful insights into the modeled system. The DCSBM approach is an example of a general framework that combines parametric random graph models and statistical process monitoring techniques for network surveillance.

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Section: Related Workmentioning

confidence: 99%

Modeling and detecting change in temporal networks via the degree corrected stochastic block model

Wilson

Stevens

Woodall

2019

Quality & Reliability Eng

109

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“…A possible way forward here is to exploit the theory developed for the individual subproblems, namely changepoint detection with the lasso (Harchaoui and Lévy-Leduc, 2010) and sparse group lasso Simon et al, 2013). Such work may build on results in the dynamic graph learning setting by Kolar andXing (2011, 2012) and Roy et al (2015).…”

Section: Discussionmentioning

confidence: 99%

Regularized Estimation of Piecewise Constant Gaussian Graphical Models: The Group-Fused Graphical Lasso

Gibberd

Nelson

2017

Journal of Computational and Graphical Statistics

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The time-evolving precision matrix of a piecewise-constant Gaussian graphical model encodes the dynamic conditional dependency structure of a multivariate time- is drawn identically from a generating distribution. Introducing sparsity and sparsedifference inducing priors we relax these assumptions and propose a novel regularized M-estimator to jointly estimate both the graph and changepoint structure. The resulting estimator possesses the ability to therefore favor sparse dependency structures and/or smoothly evolving graph structures, as required. Moreover, our approach extends current methods to allow estimation of changepoints that are grouped across multiple dependencies in a system. An efficient algorithm for estimating structure is proposed. We study the empirical recovery properties in a synthetic setting. The qualitative effect of grouped changepoint estimation is then demonstrated by applying the method on a genetic time-course data-set.

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“…In the dynamic setting, one could consider extending static neighbourhood selection methods, for instance utilising the methods of Lee et al [2016], Leonardi and Bühlmann [2016] to estimate a graph where each node may exhibit multiple change points. The work of Roy et al [2016] considers a neighbourhood selection approach for networks in the presence of a single changepoint, while Kolar and Xing [2012] consider using the fused lasso [Harchaoui and Lévy-Leduc, 2010] to estimate multiple changepoints at the node level. In the global estimation setting, Angelosante and Giannakis [2011] proposed to combine the graphical lasso with dynamic programming to estimate changepoints and graph structures.…”

Section: Literature Reviewmentioning

confidence: 99%

Consistent multiple changepoint estimation with fused Gaussian graphical models

Gibberd

Roy

2020

Ann Inst Stat Math

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We consider the consistency properties of a regularised estimator for the simultaneous identification of both changepoints and graphical dependency structure in multivariate time-series. Traditionally, estimation of Gaussian Graphical Models (GGM) is performed in an i.i.d setting. More recently, such models have been extended to allow for changes in the distribution, but only where changepoints are known a-priori. In this work, we study the Group-Fused Graphical Lasso (GFGL) which penalises partial-correlations with an L1 penalty while simultaneously inducing block-wise smoothness over time to detect multiple changepoints. We present a proof of consistency for the estimator, both in terms of changepoints, and the structure of the graphical models in each segment. arXiv:1712.05786v1 [math.ST]

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Change Point Estimation in High Dimensional Markov Random-Field Models

Cited by 49 publications

References 26 publications

Modeling and detecting change in temporal networks via the degree corrected stochastic block model

Modeling and detecting change in temporal networks via the degree corrected stochastic block model

Regularized Estimation of Piecewise Constant Gaussian Graphical Models: The Group-Fused Graphical Lasso

Consistent multiple changepoint estimation with fused Gaussian graphical models

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