论文标题
贝叶斯图形模型带有正定性的块状gibbs采样器
A positive-definiteness-assured block Gibbs sampler for Bayesian graphical models with shrinkage priors
论文作者
论文摘要
尽管Wang（2012）提出的贝叶斯图形拉索的块吉布斯采样器已被广泛应用并扩展到近年来的各种收缩率，但它具有不太明显但可能严重的劣势，即高斯图形模型中精确矩阵的正面确定性不能保证在每个周期中的gib samples samples samples samples samples samples samples samples samples sample。具体而言，如果精度矩阵的尺寸超过样本量，则几乎无法满足精度矩阵的正定确定性，并且Gibbs采样器几乎肯定会失败。在本文中，我们提出修改原始块Gibbs采样器，以使精度矩阵永远不会通过从正面确定性的域中对其进行采样而无法成为正定确定。正如我们在蒙特卡洛实验中所示的那样，这种修饰不仅稳定了采样程序，而且还显着提高了参数估计和图形结构学习的性能。我们还将提出的算法应用于每月返回数据的图形模型，其中库存数量超过样品周期，证明其稳定性和可扩展性。
Although the block Gibbs sampler for the Bayesian graphical LASSO proposed by Wang (2012) has been widely applied and extended to various shrinkage priors in recent years, it has a less noticeable but possibly severe disadvantage that the positive definiteness of a precision matrix in the Gaussian graphical model is not guaranteed in each cycle of the Gibbs sampler. Specifically, if the dimension of the precision matrix exceeds the sample size, the positive definiteness of the precision matrix will be barely satisfied and the Gibbs sampler will almost surely fail. In this paper, we propose modifying the original block Gibbs sampler so that the precision matrix never fails to be positive definite by sampling it exactly from the domain of the positive definiteness. As we have shown in the Monte Carlo experiments, this modification not only stabilizes the sampling procedure but also significantly improves the performance of the parameter estimation and graphical structure learning. We also apply our proposed algorithm to a graphical model of the monthly return data in which the number of stocks exceeds the sample period, demonstrating its stability and scalability.
