论文标题
通过收缩先验的高维回归，几乎最佳的变异推断
Nearly Optimal Variational Inference for High Dimensional Regression with Shrinkage Priors
论文作者
论文摘要
我们提出了一种具有重度线性模型推断的差异贝叶斯（VB）程序，具有重尾收缩先验，例如Student-T Prior。从理论上讲，我们建立了所提出的VB方法的一致性，并证明在正确选择先前的规格下，Vb后验的收缩率几乎是最佳的。它证明了VB推断的有效性是Markov Chain Monte Carlo（MCMC）采样的替代性。同时，与常规MCMC方法相比，VB程序达到了更高的计算效率，这大大减轻了现代机器学习应用程序（例如大规模数据分析）的计算负担。通过数值研究，我们证明了所提出的VB方法可导致计算时间较短，估计准确性较高，并且可变选择误差较低，而可变选择误差比竞争激烈的稀疏贝叶斯方法。
We propose a variational Bayesian (VB) procedure for high-dimensional linear model inferences with heavy tail shrinkage priors, such as student-t prior. Theoretically, we establish the consistency of the proposed VB method and prove that under the proper choice of prior specifications, the contraction rate of the VB posterior is nearly optimal. It justifies the validity of VB inference as an alternative of Markov Chain Monte Carlo (MCMC) sampling. Meanwhile, comparing to conventional MCMC methods, the VB procedure achieves much higher computational efficiency, which greatly alleviates the computing burden for modern machine learning applications such as massive data analysis. Through numerical studies, we demonstrate that the proposed VB method leads to shorter computing time, higher estimation accuracy, and lower variable selection error than competitive sparse Bayesian methods.
