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.

翻译：我们分析了在不同典型抽样模型下，有限支撑测度间不平衡最优传输量的插件估计量的统计性质。具体而言，我们的主要结果为质量惩罚参数$C>0$情形下，经验Kantorovich-Rubinstein（KR）距离、传输方案及重心的期望误差提供了非渐近界。我们详细研究了质量惩罚参数$C$的影响。基于此分析，我们为KR相关量建立了随机化计算方案的数学合理性，该方案可与任何精确求解器结合用于快速近似计算。通过合成与真实数据集，我们在模拟研究中实证分析了期望误差的行为，并验证了理论界的有效性。