论文标题
贝叶斯推论的普遍意义原则中位数
Generalized Median of Means Principle for Bayesian Inference
论文作者
论文摘要
鲁棒性的主题是对统计和机器学习社区的兴趣复兴。特别是，证明利用所谓估计器中位数的鲁棒算法可满足许多问题的强大性能保证，包括估计平均值，协方差结构以及线性回归。在这项工作中，我们提出了贝叶斯框架的手段中位数的扩展，从而导致了强大的后验分布的概念。特别是，我们（a）量化了离群值后部的鲁棒性，（b）表明它满足了将贝叶斯可信集与传统置信区间连接起来的伯恩斯坦 - 冯·米塞斯定理的版本，并且（c）证明我们的方法在应用程序中表现良好。
The topic of robustness is experiencing a resurgence of interest in the statistical and machine learning communities. In particular, robust algorithms making use of the so-called median of means estimator were shown to satisfy strong performance guarantees for many problems, including estimation of the mean, covariance structure as well as linear regression. In this work, we propose an extension of the median of means principle to the Bayesian framework, leading to the notion of the robust posterior distribution. In particular, we (a) quantify robustness of this posterior to outliers, (b) show that it satisfies a version of the Bernstein-von Mises theorem that connects Bayesian credible sets to the traditional confidence intervals, and (c) demonstrate that our approach performs well in applications.
