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Abstract:
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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 elementwise 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.
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