Locally associated graphical models and mixed convex exponential families
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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
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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