基于修正的Cholesky分解高维图模型贝叶斯估计

Bayesian Estimation for High Dimensional Graphical Model Based on Modified Cholesky Decomposition

文章针对高维图模型的参数估计与模型恢复问题,提出了压缩贝叶斯估计。通过构造多层贝叶斯模型,对协方差矩阵进行Colesky分解,方便地得到了重新参数化后的新参数的满足条件分布。利用Gibbs抽样,得到参数的贝叶斯估计。通过计算后验包含概率,进行模型选择。随机模拟结果表明,在高斯分布和t分布场合,压缩贝叶斯估计都有较好的稳定的表现。

This paper aims at the problem of parameter estimation for high dimensional graphical model and model recovery to propose shrinkage Bayesian estimation. And then by constructing hierarchical Bayesian model, the paper conducts a Cholesky decomposition of covariance matrix, thus conveniently obtaining the full conditional distribution of the new parameters after re-pa- rameterization. By utilizing Gibbs sampling, Bayesian estimation of parameters is obtained, and by calculating posterior probabili- ty, a model is selected. Random simulation results show that in the cases of Gaussian distribution and t distribution, shrinkage Bayesian estimation has a preferable stable performance.