Bayesian singular value regularization via a cumulative shrinkage process
Bayesian singular value regularization via a cumulative shrinkage process
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DOI：
10.1080/03610926.2020.1843055
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发表时间：
2020-06
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影响因子：
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通讯作者：
Masahiro Tanaka
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文献类型：
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作者：
Masahiro Tanaka
摘要本文提出了一种新的层次先验，用于推断含噪声的低秩矩阵。我们考虑三分量矩阵分解，在奇异值分解，其完全贝叶斯推理。建议的先验是指定的指数分布，具有尖峰和平板组件的规模混合。穗/板坯部分的重量推断使用基于累积收缩过程的特殊先验。所提出的先验被设计为越来越积极地将不太重要或基本上冗余的奇异值推向零，从而导致对低秩矩阵的更准确的估计。为了确保参数识别，我们模拟后提请从一个近似的后，其中的约束稍微放松，使用无掉头采样器。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验规范，它不会产生显着的额外计算负担。我们将所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。
Abstract 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.