Nearly optimal Bayesian shrinkage for high-dimensional regression
Nearly optimal Bayesian shrinkage for high-dimensional regression
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DOI：
10.1007/s11425-020-1912-6
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发表时间：
2017-12
期刊：
影响因子：
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通讯作者：
Qifan Song;F. Liang
中科院分区：
文献类型：
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作者：
Qifan Song;F. Liang
在过去的十年中，收缩先验在高维数据的贝叶斯分析中受到了广泛的关注。本文建立了高维线性回归模型的后验一致性，该模型具有厚而平的尾部，并且在零的一个很小的邻域内分配了足够大的概率质量。在后验模拟中，收缩先验可以获得接近最优的后验收缩率，并且与钉板先验一样具有变量选择的一致性。数值结果表明，在后验一致性条件下，贝叶斯方法在变量选择上比正则化方法如LASSO和SCAD能得到更好的结果。本文还建立了一个BvM型结果，这导致了一个方便的方法来量化回归系数估计的不确定性。
During the past decade, shrinkage priors have received much attention in Bayesian analysis of high-dimensional data. This paper establishes the posterior consistency for high-dimensional linear regression with a class of shrinkage priors, which has a heavy and flat tail and allocates a sufficiently large probability mass in a very small neighborhood of zero. While enjoying its efficiency in posterior simulations, the shrinkage prior can lead to a nearly optimal posterior contraction rate and the variable selection consistency as the spike-and-slab prior. Our numerical results show that under the posterior consistency, Bayesian methods can yield much better results in variable selection than the regularization methods such as LASSO and SCAD. This paper also establishes a BvM-type result, which leads to a convenient way of uncertainty quantification for regression coefficient estimates.