Locally associated graphical models and mixed convex exponential families

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Standard

Locally associated graphical models and mixed convex exponential families. / Lauritzen, Steffen; Zwiernik, Piotr.

In: Annals of Statistics, Vol. 50, No. 5, 27.11.2022, p. 3009-3038.

Research output: Contribution to journal › Journal article › Research › peer-review

Harvard

Lauritzen, S & Zwiernik, P 2022, 'Locally associated graphical models and mixed convex exponential families', Annals of Statistics, vol. 50, no. 5, pp. 3009-3038. https://doi.org/10.1214/22-AOS2219

APA

Lauritzen, S., & Zwiernik, P. (2022). Locally associated graphical models and mixed convex exponential families. Annals of Statistics, 50(5), 3009-3038. https://doi.org/10.1214/22-AOS2219

Vancouver

Lauritzen S, Zwiernik P. Locally associated graphical models and mixed convex exponential families. Annals of Statistics. 2022 Nov 27;50(5):3009-3038. https://doi.org/10.1214/22-AOS2219

Author

Lauritzen, Steffen ; Zwiernik, Piotr. / Locally associated graphical models and mixed convex exponential families. In: Annals of Statistics. 2022 ; Vol. 50, No. 5. pp. 3009-3038.

Bibtex

@article{38641aaad5c447e3b105ccf84b4b7d29,
title = "Locally associated graphical models and mixed convex exponential families",
abstract = "The notion of multivariate total positivity has proved to be useful in financeand psychology but may be too restrictive in other applications. In thispaper, we propose a concept of local association, where highly connectedcomponents in a graphical model are positively associated and study its properties.Our main motivation comes from gene expression data, where graphicalmodels have become a popular exploratory tool. The models are instancesof what we term mixed convex exponential families and we show that a mixeddual likelihood estimator has simple exact properties for such families aswell as asymptotic properties similar to the maximum likelihood estimator.We further relax the positivity assumption by penalizing negative partial correlationsin what we term the positive graphical lasso. Finally, we developa GOLAZO algorithm based on block-coordinate descent that applies to anumber of optimization procedures that arise in the context of graphical models,including the estimation problems described above. We derive results onexistence of the optimum for such problems.",
author = "Steffen Lauritzen and Piotr Zwiernik",
year = "2022",
month = nov,
day = "27",
doi = "10.1214/22-AOS2219",
language = "English",
volume = "50",
pages = "3009--3038",
journal = "Annals of Statistics",
issn = "0090-5364",
publisher = "Institute of Mathematical Statistics",
number = "5",

}

RIS

TY - JOUR

T1 - Locally associated graphical models and mixed convex exponential families

AU - Lauritzen, Steffen

AU - Zwiernik, Piotr

PY - 2022/11/27

Y1 - 2022/11/27

N2 - The notion of multivariate total positivity has proved to be useful in financeand psychology but may be too restrictive in other applications. In thispaper, we propose a concept of local association, where highly connectedcomponents in a graphical model are positively associated and study its properties.Our main motivation comes from gene expression data, where graphicalmodels have become a popular exploratory tool. The models are instancesof what we term mixed convex exponential families and we show that a mixeddual likelihood estimator has simple exact properties for such families aswell as asymptotic properties similar to the maximum likelihood estimator.We further relax the positivity assumption by penalizing negative partial correlationsin what we term the positive graphical lasso. Finally, we developa GOLAZO algorithm based on block-coordinate descent that applies to anumber of optimization procedures that arise in the context of graphical models,including the estimation problems described above. We derive results onexistence of the optimum for such problems.

AB - The notion of multivariate total positivity has proved to be useful in financeand psychology but may be too restrictive in other applications. In thispaper, we propose a concept of local association, where highly connectedcomponents in a graphical model are positively associated and study its properties.Our main motivation comes from gene expression data, where graphicalmodels have become a popular exploratory tool. The models are instancesof what we term mixed convex exponential families and we show that a mixeddual likelihood estimator has simple exact properties for such families aswell as asymptotic properties similar to the maximum likelihood estimator.We further relax the positivity assumption by penalizing negative partial correlationsin what we term the positive graphical lasso. Finally, we developa GOLAZO algorithm based on block-coordinate descent that applies to anumber of optimization procedures that arise in the context of graphical models,including the estimation problems described above. We derive results onexistence of the optimum for such problems.

U2 - 10.1214/22-AOS2219

DO - 10.1214/22-AOS2219

M3 - Journal article

VL - 50

SP - 3009

EP - 3038

JO - Annals of Statistics

JF - Annals of Statistics

SN - 0090-5364

IS - 5

ER -

ID: 323623210