论文标题
有限空间上不平衡的Kantorovich-Rubinstein距离，计划和Barycenter：统计观点
Unbalanced Kantorovich-Rubinstein distance, plan, and barycenter on finite spaces: A statistical perspective
论文作者
论文摘要
我们分析了插入式估计器的统计特性，用于不同原型采样模型中有限支持的措施之间的不平衡最佳运输量。具体而言，我们的主要结果在经验的Kantorovich-Rubinstein（KR）距离，计划和Barycenters的预期误差上提供了非反应界限，以进行质量罚款参数$ C> 0 $。详细研究了质量罚款参数$ c $的影响。基于此分析，我们在数学上证明了KR数量的随机计算方案合理的合理性，这些计算方案可与任何确切的求解器结合使用，用于快速近似计算。使用合成和实际数据集，我们经验分析了模拟研究中预期错误的行为，并说明了我们理论界限的有效性。
We analyze statistical properties of plug-in estimators for unbalanced optimal transport quantities between finitely supported measures in different prototypical sampling models. Specifically, our main results provide non-asymptotic bounds on the expected error of empirical Kantorovich-Rubinstein (KR) distance, plans, and barycenters for mass penalty parameter $C>0$. The impact of the mass penalty parameter $C$ is studied in detail. Based on this analysis, we mathematically justify randomized computational schemes for KR quantities which can be used for fast approximate computations in combination with any exact solver. Using synthetic and real datasets, we empirically analyze the behavior of the expected errors in simulation studies and illustrate the validity of our theoretical bounds.
