Consistent Group Selection with Bayesian High Dimensional Modeling
Consistent Group Selection with Bayesian High Dimensional Modeling
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DOI：
10.1214/19-ba1178
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发表时间：
2020-09
影响因子：
4.4
通讯作者：
Xinming Yang;N. Narisetty
中科院分区：
文献类型：
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作者：
Xinming Yang;N. Narisetty
.在许多高维协变量的应用中，协变量被自然地构造成不同的组，这些组可以用于执行有效的统计推断。本文提出了一种具有spike和slab先验指定的贝叶斯分层模型，用于高维线性回归模型中的组选择。虽然有几种惩罚方法和最近提出的一些贝叶斯方法用于群体选择，但贝叶斯方法的理论特性尚未得到广泛研究。在本文中，我们提供了新的理论结果，组选择一致性下的穗和板先验表明，所提出的贝叶斯方法相比，惩罚方法具有优势。我们的理论结果适应设计矩阵上的不确定性条件，并可以应用于常用的统计模型，如非参数加性模型，其中非常有限的理论结果可用于贝叶斯方法。鸟枪随机搜索算法是通过我们所提出的方法的实施。我们通过仿真研究表明，所提出的方法具有更好的性能相比，现有的各种方法的组选择。
. In many applications with high dimensional covariates, the covariates are naturally structured into different groups which can be used to perform efficient statistical inference. We propose a Bayesian hierarchical model with a spike and slab prior specification to perform group selection in high dimensional linear regression models. While several penalization methods and more recently, some Bayesian approaches are proposed for group selection, theoretical properties of Bayesian approaches have not been studied extensively. In this paper, we provide novel theoretical results for group selection consistency under spike and slab priors which demonstrate that the proposed Bayesian approach has advantages compared to penalization approaches. Our theoretical results accommodate flexible conditions on the design matrix and can be applied to commonly used statistical models such as nonparametric additive models for which very limited theoretical results are available for the Bayesian methods. A shotgun stochastic search algorithm is adopted for the implementation of our proposed approach. We illustrate through simulation studies that the proposed method has better performance for group selection compared to a variety of existing methods.