论文标题
通过筛选的β-混合事先进行的稀疏协方差矩阵的可扩展和最佳贝叶斯推断
Scalable and optimal Bayesian inference for sparse covariance matrices via screened beta-mixture prior
论文作者
论文摘要
在本文中，我们提出了一种可扩展的贝叶斯方法，用于通过将连续的收缩率与筛选程序结合在一起，以进行稀疏协方差矩阵估计。在过程的第一步中，根据其样品相关性筛选了具有较小相关性的非对角线元素。在第二步中，协方差的后部与固定在$ 0 $的筛选元素的后部计算为beta-mixture之前。协方差的筛选元素显着提高了后验计算的效率。仿真研究和实际数据应用显示，所提出的方法可用于“大P，小N”的高维问题。在本文的一些示例中，可以在合理的时间内计算提出的方法，而其他现有的贝叶斯方法则可以计算。所提出的方法还具有理论的理论属性。筛选程序具有确定的筛选属性和选择一致性，并且后部在Frobeninus Norm下具有最佳的最小值或几乎最小值收敛速率。
In this paper, we propose a scalable Bayesian method for sparse covariance matrix estimation by incorporating a continuous shrinkage prior with a screening procedure. In the first step of the procedure, the off-diagonal elements with small correlations are screened based on their sample correlations. In the second step, the posterior of the covariance with the screened elements fixed at $0$ is computed with the beta-mixture prior. The screened elements of the covariance significantly increase the efficiency of the posterior computation. The simulation studies and real data applications show that the proposed method can be used for the high-dimensional problem with the `large p, small n'. In some examples in this paper, the proposed method can be computed in a reasonable amount of time, while no other existing Bayesian methods can be. The proposed method has also sound theoretical properties. The screening procedure has the sure screening property and the selection consistency, and the posterior has the optimal minimax or nearly minimax convergence rate under the Frobeninus norm.
