Unified Bayesian theory of sparse linear regression with nuisance parameters
Unified Bayesian theory of sparse linear regression with nuisance parameters
复制标题
带有干扰参数的稀疏线性回归的统一贝叶斯理论
DOI：
10.1214/21-ejs1855
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发表时间：
2021
影响因子：
1.1
通讯作者：
S. Ghosal
中科院分区：
文献类型：
--
作者：
Seonghyun Jeong;S. Ghosal
本文研究了高维高斯稀疏回归的贝叶斯过程在干扰参数未知时的频率渐近性质。营养参数可以是有限维、高维或无限维的。零和连续分布的点质量的混合物用于稀疏回归系数的先验分布，并且适当的先验分布用于滋扰参数。稀疏回归系数的最佳后验收缩，妨碍滋扰参数的存在下，也检查和讨论。结果表明，该过程产生强大的模型选择的一致性。稀疏回归系数的Bernstein-von Mises型定理也得到了不确定性量化通过可靠的集合，保证频率覆盖。许多例子的渐近性质进行了研究，使用本研究中开发的理论。
We study frequentist asymptotic properties of Bayesian procedures for high-dimensional Gaussian sparse regression when unknown nuisance parameters are involved. Nuisance parameters can be finite-, high-, or infinite-dimensional. A mixture of point masses at zero and continuous distributions is used for the prior distribution on sparse regression coefficients, and appropriate prior distributions are used for nuisance parameters. The optimal posterior contraction of sparse regression coefficients, hampered by the presence of nuisance parameters, is also examined and discussed. It is shown that the procedure yields strong model selection consistency. A Bernstein-von Mises-type theorem for sparse regression coefficients is also obtained for uncertainty quantification through credible sets with guaranteed frequentist coverage. Asymptotic properties of numerous examples are investigated using the theories developed in this study.
DOI：
10.1007/s11425-020-1912-6
发表时间：
2017-12
期刊：
Science China Mathematics
影响因子：
--
作者：
Qifan Song;F. Liang
通讯作者：
Qifan Song;F. Liang