论文标题
根据坐标级腐败的强大平均估计
On Robust Mean Estimation under Coordinate-level Corruption
论文作者
论文摘要
我们研究了强大的平均估计问题，并引入了一种基于锤距离的新型分配转移量度的坐标水平损坏的度量。我们表明，这项措施产生的对手模型比以前的工作中使用的腐败更现实，并对这些环境中强大的平均估计进行了信息理论分析。我们表明，对于结构化分布，利用结构在理论上产生信息的方法更准确。当数据清洁启发的方法首先修复输入数据中的损坏，然后执行强大的平均估计可以匹配我们分析的信息理论界限时，我们还专注于可靠的平均估计和研究的实用算法。我们最终在实验上证明，这种两步方法的表现优于结构 - 不合稳定的鲁棒估计，甚至为高质量损坏提供了准确的平均估计。
We study the problem of robust mean estimation and introduce a novel Hamming distance-based measure of distribution shift for coordinate-level corruptions. We show that this measure yields adversary models that capture more realistic corruptions than those used in prior works, and present an information-theoretic analysis of robust mean estimation in these settings. We show that for structured distributions, methods that leverage the structure yield information theoretically more accurate mean estimation. We also focus on practical algorithms for robust mean estimation and study when data cleaning-inspired approaches that first fix corruptions in the input data and then perform robust mean estimation can match the information theoretic bounds of our analysis. We finally demonstrate experimentally that this two-step approach outperforms structure-agnostic robust estimation and provides accurate mean estimation even for high-magnitude corruption.
