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Lingrui Gan

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JMLR Journal 2021 Journal Article

GemBag: Group Estimation of Multiple Bayesian Graphical Models

Xinming Yang
Lingrui Gan
Naveen N. Narisetty
Feng Liang

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 sup-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. [abs] [ pdf ][ bib ] &copy JMLR 2021. ( edit, beta )

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NeurIPS Conference 2019 Conference Paper

Bayesian Joint Estimation of Multiple Graphical Models

Lingrui Gan
Xinming Yang
Naveen Narisetty
Feng Liang

In this paper, we propose a novel Bayesian group regularization method based on the spike and slab Lasso priors for jointly estimating multiple graphical models. The proposed method can be used to estimate the common sparsity structure underlying the graphical models while capturing potential heterogeneity of the precision matrices corresponding to those models. Our theoretical results show that the proposed method enjoys the optimal rate of convergence in $\ell_\infty$ norm for estimation consistency and has a strong structure recovery guarantee even when the signal strengths over different graphs are heterogeneous. Through simulation studies and an application to the capital bike-sharing network data, we demonstrate the competitive performance of our method compared to existing alternatives.

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