On the Rate of Convergence of Empirical Measures in infinity-transportation Distance

Trillos Nicolas Garcia; Slepcev Dejan

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On the Rate of Convergence of Empirical Measures in infinity-transportation Distance

机译：无限运输距离中经验测度的收敛速度

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摘要

We consider random i.i.d. samples of absolutely continuous measures on bounded connected domains. We prove an upper bound on the infinity-transportation distance between the measure and the empirical measure of the sample. The bound is optimal in terms of scaling with the number of sample points.

机译：我们考虑随机i.d.有界连通域上绝对连续测度的样本。我们证明了量度和样本的经验量度之间的无穷远传输距离的上限。在根据采样点的数量进行缩放方面，边界是最佳的。

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来源
《Canadian Journal of Mathematics》 |2015年第6期|共26页
作者
Trillos Nicolas Garcia; Slepcev Dejan;
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正文语种 eng
中图分类数学;
关键词
optimal transportation; optimal matching; infinity transportation distance; min-max distance; empirical measure;

机译：最优运输;最优匹配;无限运输距离;最小最大距离;经验测度;

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专利

1. On the Rate of Convergence of Empirical Measures in infinity-transportation Distance [J] . Trillos Nicolas Garcia, Slepcev Dejan Canadian Journal of Mathematics . 2015,第6期

机译：无限运输距离中经验测度的收敛速度
2. ON THE RATE OF CONVERGENCE OF EMPIRICAL MEASURE IN infinity-WASSERSTEIN DISTANCE FOR UNBOUNDED DENSITY FUNCTION [J] . Liu Anning, Liu Jian-Guo, Lu Yulong Quarterly of Applied Mathematics . 2019,第4期

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3. On the rate of convergence in Wasserstein distance of the empirical measure [J] . Fournier Nicolas, Guillin Arnaud Probability Theory and Related Fields . 2015,第3a4期

机译：关于Wasserstein距离的收敛速度的经验测度
4. Consistency and convergence rates in Lagrangian empirical design of variable-rate vector quantizers [C] . Tamas Linder IEEE International Symposium on Information Theory . 2002

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5. Strategic groups of countries: An empirical study of government policies toward foreign direct investment and their convergence over time. [D] . Mileski, Joan Patricia. 2000

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6. Convergence Rates for Empirical Estimation of Binary Classification Bounds [O] . Salimeh Yasaei Sekeh, Morteza Noshad, Kevin R. Moon, 2019

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7. Sharp asymptotic and finite-sample rates of convergence of empirical measures in Wasserstein distance [O] . Jonathan Weed, Francis Bach 2019

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On the Rate of Convergence of Empirical Measures in infinity-transportation Distance

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