Bayesian Graphical Lasso Models and Efficient Posterior Computation
Bayesian Graphical Lasso Models and Efficient Posterior Computation
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DOI：
10.1214/12-ba729
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发表时间：
2012-01-01
影响因子：
4.4
通讯作者：
Wang, Hao
中科院分区：
文献类型：
--
作者：
Wang, Hao
最近，图形套索过程已成为流行的估计高斯图模型。在本文中，我们介绍了一个完全贝叶斯处理的图形套索模型。我们首先研究了图形套索之前，一直相对未被探索。使用数据增强，我们开发了一个简单但高效的块吉布斯采样器来模拟协方差矩阵。然后，我们将贝叶斯图形套索推广到贝叶斯自适应图形套索。最后，我们说明和比较结果，从我们的方法得到的那些使用标准的图形套索程序的真实的和模拟数据。在协方差矩阵估计和图形结构学习方面，贝叶斯自适应图形套索似乎是一系列频率论和贝叶斯方法中的最佳整体表现。
Recently, the graphical lasso procedure has become popular in estimating Gaussian graphical models. In this paper, we introduce a fully Bayesian treatment of graphical lasso models. We first investigate the graphical lasso prior that has been relatively unexplored. Using data augmentation, we develop a simple but highly efficient block Gibbs sampler for simulating covariance matrices. We then generalize the Bayesian graphical lasso to the Bayesian adaptive graphical lasso. Finally, we illustrate and compare the results from our approach to those obtained using the standard graphical lasso procedures for real and simulated data. In terms of both covariance matrix estimation and graphical structure learning, the Bayesian adaptive graphical lasso appears to be the top overall performer among a range of frequentist and Bayesian methods.