We develop a novel full-Bayesian approach for multiple correlated precision matrices, called multiple Graphical Horseshoe (mGHS). The proposed approach relies on a novel multivariate shrinkage prior based on the Horseshoe prior that borrows strength and shares sparsity patterns across groups, improving posterior edge selection when the precision matrices are similar. On the other hand, there is no loss of performance when the groups are independent. Moreover, mGHS provides a similarity matrix estimate, useful for understanding network similarities across groups. We implement an efficient Metropolis-within-Gibbs for posterior inference; specifically, local variance parameters are updated via a novel and efficient modified rejection sampling algorithm that samples from a three-parameter Gamma distribution. The method scales well with respect to the number of variables and provides one of the fastest full-Bayesian approaches for the estimation of multiple precision matrices. Finally, edge selection is performed with a novel approach based on model cuts. We empirically demonstrate that mGHS outperforms competing approaches through both simulation studies and an application to a bike-sharing dataset.
翻译:我们为多个相关精密矩阵开发了新型全巴耶式全方位方法,称为多重图形马蹄(MGHS) 。 提议的方法依赖于基于马蹄(Horsehoe before strange) 之前的新的多变缩缩法, 前者在各组间借用强度和共享聚度模式, 后者在精确矩阵相似时改进后边缘选择。 另一方面, 当组间独立时, 其性能没有损失。 此外, 兆赫( mGHS) 提供了相似性矩阵估计, 有助于理解各组间网络的相似性。 我们实施了高效的大都会- 内 Gibbbs, 用于事后推断; 具体地, 本地差异参数通过新颖而高效的修改的拒绝采样法更新, 样本来自3个参数 Gamma 分布。 有关变量数量的方法比例, 提供了最快的全巴耶斯方法之一, 用于估算多个精准矩阵。 最后, 以基于模型切割的新方法进行边缘选择。 我们从经验上证明, MGHS 超越了通过模拟研究和自行车共享数据集应用的竞合方法。