论文标题
B-Concord-可扩展的贝叶斯高维精度矩阵估计过程
B-CONCORD -- A scalable Bayesian high-dimensional precision matrix estimation procedure
论文作者
论文摘要
在高维缩放下对精度矩阵的稀疏估计构成了统计和机器学习中的规范问题。已经开发了许多基于回归和可能性的方法，许多经常主义者和一些贝叶斯人已经发展出来。贝叶斯方法通过后验分布提供了模型参数的直接不确定性量化，因此不需要第二轮计算来获得模型参数及其置信区间的依据估计。但是，对于涉及500多个变量的设置，它们在计算上昂贵。为此，我们开发了当前问题的B-Concord，这是Khare等人引入的凸相关选择方法（Concord）的贝叶斯类似物。 （2015）。 B-concord利用一致性的可能性函数以及尖峰和slab先验分布，以在精度矩阵参数中诱导稀疏性。我们在高维缩放下建立模型选择和估计一致性；此外，我们开发了一种仅改写精度矩阵的非零参数的过程，从而导致有限样本中的估计值有显着改善。广泛的数值工作说明了相对于竞争贝叶斯方法及其准确性的拟议方法的计算可扩展性。
Sparse estimation of the precision matrix under high-dimensional scaling constitutes a canonical problem in statistics and machine learning. Numerous regression and likelihood based approaches, many frequentist and some Bayesian in nature have been developed. Bayesian methods provide direct uncertainty quantification of the model parameters through the posterior distribution and thus do not require a second round of computations for obtaining debiased estimates of the model parameters and their confidence intervals. However, they are computationally expensive for settings involving more than 500 variables. To that end, we develop B-CONCORD for the problem at hand, a Bayesian analogue of the CONvex CORrelation selection methoD (CONCORD) introduced by Khare et al. (2015). B-CONCORD leverages the CONCORD generalized likelihood function together with a spike-and-slab prior distribution to induce sparsity in the precision matrix parameters. We establish model selection and estimation consistency under high-dimensional scaling; further, we develop a procedure that refits only the non-zero parameters of the precision matrix, leading to significant improvements in the estimates in finite samples. Extensive numerical work illustrates the computational scalability of the proposed approach vis-a-vis competing Bayesian methods, as well as its accuracy.
