TY - JOUR
T1 - GemBag
T2 - Group estimation of multiple bayesian graphical models
AU - Yang, Xinming
AU - Gan, Lingrui
AU - Narisetty, Naveennaidu
AU - Liang, Feng
N1 - Funding Information:
We sincerely thank the editor and three reviewers for their insightful comments that improved the manuscript. Naveen Narisetty gratefully acknowledges partial funding support from NSF grants DMS-1811768 and CAREER-1943500. Feng Liang gratefully acknowledges funding support from NSF-DMS 1916472.
Publisher Copyright:
© 2021 Xinming Yang, Lingrui Gan, Naveen N. Narisetty, and Feng Liang.
PY - 2021
Y1 - 2021
N2 - In this paper, we propose a novel hierarchical Bayesian model and an efficient estimation method for the problem of joint estimation of multiple graphical models, which have similar but different sparsity structures and signal strength. Our proposed hierarchical Bayesian model is well suited for sharing of sparsity structures, and our procedure, called as GemBag, is shown to enjoy optimal theoretical properties in terms of ℓ8 norm estimation accuracy and correct recovery of the graphical structure even when some of the signals are weak. Although optimization of the posterior distribution required for obtaining our proposed estimator is a non-convex optimization problem, we show that it turns out to be convex in a large constrained space facilitating the use of computationally efficient algorithms. Through extensive simulation studies and an application to a bike sharing data set, we demonstrate that the proposed GemBag procedure has strong empirical performance in comparison with alternative methods.
AB - In this paper, we propose a novel hierarchical Bayesian model and an efficient estimation method for the problem of joint estimation of multiple graphical models, which have similar but different sparsity structures and signal strength. Our proposed hierarchical Bayesian model is well suited for sharing of sparsity structures, and our procedure, called as GemBag, is shown to enjoy optimal theoretical properties in terms of ℓ8 norm estimation accuracy and correct recovery of the graphical structure even when some of the signals are weak. Although optimization of the posterior distribution required for obtaining our proposed estimator is a non-convex optimization problem, we show that it turns out to be convex in a large constrained space facilitating the use of computationally efficient algorithms. Through extensive simulation studies and an application to a bike sharing data set, we demonstrate that the proposed GemBag procedure has strong empirical performance in comparison with alternative methods.
KW - Bayesian regularization
KW - EM algorithm
KW - Graphical models
KW - Non-convex optimization
KW - Selection consistency
KW - Spike-and-slab priors
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M3 - Article
AN - SCOPUS:85105877884
SN - 1532-4435
VL - 22
JO - Journal of Machine Learning Research
JF - Journal of Machine Learning Research
ER -