论文标题
高维逻辑回归的尖峰和平板变化贝叶
Spike and slab variational Bayes for high dimensional logistic regression
论文作者
论文摘要
变异贝叶斯（VB）是马尔可夫链蒙特卡洛（Monte Carlo）的流行可扩展替代品，用于贝叶斯推断。我们研究了稀疏高维逻辑回归中广泛使用的贝叶斯模型选择先验的平均场尖峰和平板VB近似。我们在$ \ ell_2 $中为VB后验提供了非反应理论保证，以及稀疏真理的预测损失，给出了最佳（minimax）收敛速率。由于VB算法不取决于未知的真理来实现最佳性，因此我们的结果揭示了有效的先前选择。在数值研究中，我们证实了VB算法在常见的稀疏VB方法上的性能提高。
Variational Bayes (VB) is a popular scalable alternative to Markov chain Monte Carlo for Bayesian inference. We study a mean-field spike and slab VB approximation of widely used Bayesian model selection priors in sparse high-dimensional logistic regression. We provide non-asymptotic theoretical guarantees for the VB posterior in both $\ell_2$ and prediction loss for a sparse truth, giving optimal (minimax) convergence rates. Since the VB algorithm does not depend on the unknown truth to achieve optimality, our results shed light on effective prior choices. We confirm the improved performance of our VB algorithm over common sparse VB approaches in a numerical study.
