论文标题
通过累积收缩过程，贝叶斯单数值正则化
Bayesian Singular Value Regularization via a Cumulative Shrinkage Process
论文作者
论文摘要
这项研究提出了一个新的分层先验，用于推断用噪声测量的低级矩阵。我们考虑三成分矩阵分解，如奇异值分解及其完全贝叶斯的推断。提出的先验是由具有尖峰和平板成分的指数分布的比例混合物指定的。根据累积收缩过程，使用特殊先验推断出尖峰/平板零件的重量。提出的先验旨在越来越积极地推动较少的重要性或本质上是冗余的奇异值向零，从而更准确地估计了低级矩阵。为了确保参数识别，我们模拟了从近似后部绘制的后验，其中约束使用No-U-Turn采样器略微放松。通过一组仿真研究，我们表明我们的建议具有替代性先前规格的竞争力，并且不会产生重大的额外计算负担。我们将拟议的方法应用于美国的部门工业生产，以分析大节日期间的结构变化。
This study proposes a novel hierarchical prior for inferring possibly low-rank matrices measured with noise. We consider three-component matrix factorization, as in singular value decomposition, and its fully Bayesian inference. The proposed prior is specified by a scale mixture of exponential distributions that has spike and slab components. The weights for the spike/slab parts are inferred using a special prior based on a cumulative shrinkage process. The proposed prior is designed to increasingly aggressively push less important, or essentially redundant, singular values toward zero, leading to more accurate estimates of low-rank matrices. To ensure the parameter identification, we simulate posterior draws from an approximated posterior, in which the constraints are slightly relaxed, using a No-U-Turn sampler. By means of a set of simulation studies, we show that our proposal is competitive with alternative prior specifications and that it does not incur significant additional computational burden. We apply the proposed approach to sectoral industrial production in the United States to analyze the structural change during the Great Moderation period.
