论文标题
Tukey中位数什么时候起作用？
When does the Tukey median work?
论文作者
论文摘要
我们在总变化（TV）距离损坏下分析了Tukey中位估计器的性能。先前的结果表明，在Huber的添加腐败模型下，对于高维半空间与对称分布的分解点为1/3。我们表明，在电视损坏下，对于同一组发行版，崩溃点将减少到1/4。我们还表明，某些投影算法可以达到1/2的最佳分解点。 Tukey中值估计器和投影算法都在维度上实现了样品复杂性线性。
We analyze the performance of the Tukey median estimator under total variation (TV) distance corruptions. Previous results show that under Huber's additive corruption model, the breakdown point is 1/3 for high-dimensional halfspace-symmetric distributions. We show that under TV corruptions, the breakdown point reduces to 1/4 for the same set of distributions. We also show that a certain projection algorithm can attain the optimal breakdown point of 1/2. Both the Tukey median estimator and the projection algorithm achieve sample complexity linear in dimension.
