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Consistent multiple changepoint estimation with fused Gaussian graphical models

Research output: Contribution to Journal/Magazine › Journal article › peer-review

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Consistent multiple changepoint estimation with fused Gaussian graphical models. / Gibberd, A.; Roy, S.
In: Annals of the Institute of Statistical Mathematics, 17.03.2020.

Research output: Contribution to Journal/Magazine › Journal article › peer-review

Harvard

Gibberd, A & Roy, S 2020, 'Consistent multiple changepoint estimation with fused Gaussian graphical models', Annals of the Institute of Statistical Mathematics. https://doi.org/10.1007/s10463-020-00749-0

APA

Gibberd, A., & Roy, S. (2020). Consistent multiple changepoint estimation with fused Gaussian graphical models. Annals of the Institute of Statistical Mathematics. Advance online publication. https://doi.org/10.1007/s10463-020-00749-0

Vancouver

Gibberd A, Roy S. Consistent multiple changepoint estimation with fused Gaussian graphical models. Annals of the Institute of Statistical Mathematics. 2020 Mar 17. Epub 2020 Mar 17. doi: 10.1007/s10463-020-00749-0

Author

Gibberd, A. ; Roy, S. / Consistent multiple changepoint estimation with fused Gaussian graphical models. In: Annals of the Institute of Statistical Mathematics. 2020.

Bibtex

@article{0ff888b04ca9432c8923fba8a7568d85,
title = "Consistent multiple changepoint estimation with fused Gaussian graphical models",
abstract = "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 primarily 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. We contrast our results, which are based on a global, i.e. graph-wide likelihood, with those previously obtained for performing dynamic graph estimation at a node-wise (or neighbourhood) level.",
keywords = "Asymptotics, Changepoint, Graphical model, Regularisation",
author = "A. Gibberd and S. Roy",
note = "The final publication is available at Springer via http://dx.doi.org/10.1007/s10463-020-00749-0",
year = "2020",
month = mar,
day = "17",
doi = "10.1007/s10463-020-00749-0",
language = "English",
journal = "Annals of the Institute of Statistical Mathematics",
issn = "0020-3157",
publisher = "Springer Netherlands",

}

RIS

TY - JOUR

T1 - Consistent multiple changepoint estimation with fused Gaussian graphical models

AU - Gibberd, A.

AU - Roy, S.

N1 - The final publication is available at Springer via http://dx.doi.org/10.1007/s10463-020-00749-0

PY - 2020/3/17

Y1 - 2020/3/17

N2 - 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 primarily 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. We contrast our results, which are based on a global, i.e. graph-wide likelihood, with those previously obtained for performing dynamic graph estimation at a node-wise (or neighbourhood) level.

AB - 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 primarily 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. We contrast our results, which are based on a global, i.e. graph-wide likelihood, with those previously obtained for performing dynamic graph estimation at a node-wise (or neighbourhood) level.

KW - Asymptotics

KW - Changepoint

KW - Graphical model

KW - Regularisation

U2 - 10.1007/s10463-020-00749-0

DO - 10.1007/s10463-020-00749-0

M3 - Journal article

JO - Annals of the Institute of Statistical Mathematics

JF - Annals of the Institute of Statistical Mathematics

SN - 0020-3157

ER -