GemBag: Group Estimation of Multiple Bayesian Graphical Models
GemBag: Group Estimation of Multiple Bayesian Graphical Models
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发表时间：
2021
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通讯作者：
Xinming Yang;Lingrui Gan;N. Narisetty;Feng Liang
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作者：
Xinming Yang;Lingrui Gan;N. Narisetty;Feng Liang
针对稀疏结构和信号强度相似但不同的多个图模型的联合估计问题，提出了一种新的分层贝叶斯模型和一种有效的估计方法.我们提出的分层贝叶斯模型是非常适合共享的稀疏结构，我们的程序，称为GemBag，被证明享有最佳的理论属性（cid：96）8范数估计精度和正确的恢复的图形结构，即使当一些信号是弱的。虽然获得我们提出的估计所需的后验分布的优化是一个非凸优化问题，我们表明，它原来是凸的，在一个大的约束空间，方便使用的计算效率的算法。通过广泛的模拟研究和应用程序的自行车共享数据集，我们表明，所提出的GemBag程序具有较强的经验性能与其他方法相比。
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 (cid:96) 8 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.