Uniform bounds for robust mean estimators
Uniform bounds for robust mean estimators
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发表时间：
2018-12
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通讯作者：
Stanislav Minsker
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作者：
Stanislav Minsker
本文专门介绍了在对基础分布的最低假设下提供强大的非反应保证的平均值估计量。拟议技术背后的主要思想是基于桥接对称性和鲁棒性的概念。我们表明，现有的方法，例如平均值和Catoni的估计器，通常可以看作是我们建筑的特殊情况。本文的主要贡献是统一的范围证明了由提议的估计器定义的随机过程的偏差。此外，我们将结果扩展到了对抗性污染的情况，在这种情况下，观察值的持续部分被任意损坏。最后，我们将方法应用于鲁棒的多元平均估计问题，并表明获得的不平等达到了对损坏样本比例的最佳依赖性。
This paper is devoted to the estimators of the mean that provide strong non-asymptotic guarantees under minimal assumptions on the underlying distribution. The main ideas behind proposed techniques are based on bridging the notions of symmetry and robustness. We show that existing methods, such as median-of-means and Catoni's estimators, can often be viewed as special cases of our construction. The main contribution of the paper is the proof of uniform bounds for the deviations of the stochastic process defined by proposed estimators. Moreover, we extend our results to the case of adversarial contamination where a constant fraction of the observations is arbitrarily corrupted. Finally, we apply our methods to the problem of robust multivariate mean estimation and show that obtained inequalities achieve optimal dependence on the proportion of corrupted samples.