Gaussian concentration graphical models are one of the most popular models for sparse covariance estimation with high-dimensional data. In recent years, much research has gone into development of methods which facilitate Bayesian inference for these models under the standard $G$-Wishart prior. However, convergence properties of the resulting posteriors are not completely understood, particularly in high-dimensional settings. In this paper, we derive high-dimensional posterior convergence rates for the class of decomposable concentration graphical models. A key initial step which facilitates our analysis is transformation to the Cholesky factor of the inverse covariance matrix. As a by-product of our analysis, we also obtain convergence rates for the corresponding maximum likelihood estimator.
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机译：高斯浓度图形模型是使用高维数据进行稀疏协方差估计的最受欢迎模型之一。近年来，在标准$ G $ -Wishart的支持下，促进了这些模型的贝叶斯推理的方法的开发已经进行了大量研究。然而，所产生的后代的会聚特性还没有被完全理解，特别是在高维环境中。在本文中，我们为可分解浓度图形模型类推导了高维后验收敛率。有助于我们进行分析的关键初始步骤是转换为逆协方差矩阵的Cholesky因子。作为我们分析的副产品，我们还获得了相应最大似然估计的收敛速度。
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