Bayesian Eigenvalue Regularization via Cumulative Shrinkage Process
Bayesian Eigenvalue Regularization via Cumulative Shrinkage Process
复制标题
DOI：
--
复制
发表时间：
2020-06
期刊：
影响因子：
--
通讯作者：
Masahiro Tanaka
中科院分区：
文献类型：
--
作者：
Masahiro Tanaka
本研究提出了一种新的层次先验来推断可能含有噪声的低秩矩阵。我们考虑奇异值分解中的三分量矩阵分解及其完全贝叶斯推理。所提出的先验是由具有尖峰和板分量的指数分布的尺度混合指定的。钉/板零件的重量是使用基于累积收缩过程的特殊先验来推断的。所提出的先验被设计为越来越积极地将不太重要或本质上冗余的特征值推向零，从而导致对低秩矩阵的更准确估计。为了确保参数识别，我们使用No-U-Turn采样器从约束稍微放松的近似后验中模拟后验抽取。通过一组模拟研究，我们表明，我们的建议是有竞争力的替代先前的规范，它不会产生显著的额外计算负担。我们将提出的方法应用于美国的部门工业生产，以分析大缓和时期的结构变化。
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, eigenvalues 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.