Bayesian Joint Estimation of Multiple Graphical Models
Bayesian Joint Estimation of Multiple Graphical Models
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发表时间：
2019
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通讯作者：
Lingrui Gan;Xinming Yang;N. Narisetty;Feng Liang
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作者：
Lingrui Gan;Xinming Yang;N. Narisetty;Feng Liang
本文提出了一种新的基于spike和slab Lasso先验的贝叶斯群正则化方法，用于联合估计多个图形模型。该方法可用于估计图形模型的共同稀疏性结构，同时捕获与这些模型对应的精度矩阵的潜在异质性。理论结果表明，该方法在$\ell_\infty$范数下具有最优的估计一致性收敛速度，即使不同图上的信号强度是异构的，也具有较强的结构恢复保证。通过仿真研究和对首都共享单车网络数据的应用，我们证明了与现有替代方案相比，我们的方法具有竞争力。
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.