WEAK OPTIMAL TRANSPORT WITH UNNORMALIZED KERNELS

被引：2
|
作者：
Chone, Philippe [1 ]
Gozlan, Nathael [2 ]
Kramarz, Francis [3 ,4 ]
机构：
[1] CREST, ENSAE, Inst Polytech Paris, Paris, France
[2] Univ Paris Cite, MAP5, CNRS, F-75006 Paris, France
[3] CREST, Inst Polytech Paris, ENSAE, Paris, France
[4] Uppsala Univ, Dept Econ, Uppsala, Sweden
来源：
SIAM JOURNAL ON MATHEMATICAL ANALYSIS | 2023年 / 55卷 / 06期
基金：
欧洲研究理事会;
关键词：
optimal transport; weak optimal transport; duality; convex order; Strassen's theorem; PROBABILITY-MEASURES; REARRANGEMENT; COSTS;
D O I：
10.1137/22M1501301
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We introduce a new variant of the weak optimal transport problem where mass is distributed from one space to the other through unnormalized kernels. We give sufficient conditions for primal attainment and prove a dual formula for this transport problem. We also obtain dual attainment conditions for some specific cost functions. As a byproduct, we obtain a transport characterization of the stochastic order defined by convex positively 1-homogenous functions, in the spirit of the Strassen theorem for convex domination.
引用
收藏
页码：6039 / 6092
页数：54
相关论文
共 50 条
  • [31] WEAK SEDIMENT TRANSPORT
    PAZIS, GC
    GRAF, WH
    JOURNAL OF THE HYDRAULICS DIVISION-ASCE, 1977, 103 (07): : 799 - 802
  • [32] WEAK SEDIMENT TRANSPORT
    PAZIS, GC
    GRAF, WH
    JOURNAL OF THE HYDRAULICS DIVISION-ASCE, 1979, 105 (01): : 108 - 109
  • [33] Sparse kernels for Bayes optimal discriminant analysis
    Hamsici, Onur C.
    Martinez, Aleix M.
    2007 IEEE CONFERENCE ON COMPUTER VISION AND PATTERN RECOGNITION, VOLS 1-8, 2007, : 3132 - +
  • [34] Optimal Kernel in a Class of Kernels with an Invariant Metric
    Tanaka, Akira
    Imai, Hideyuki
    Kudo, Mineichi
    Miyakoshi, Masaaki
    STRUCTURAL, SYNTACTIC, AND STATISTICAL PATTERN RECOGNITION, 2008, 5342 : 530 - 539
  • [35] OPTIMAL KERNELS WHEN ESTIMATING NONSMOOTH DENSITIES
    SWANEPOEL, JWH
    COMMUNICATIONS IN STATISTICS-THEORY AND METHODS, 1987, 16 (06) : 1835 - 1848
  • [36] Optimal rates of distributed regression with imperfect kernels
    Sun, Hongwei
    Wu, Qiang
    Journal of Machine Learning Research, 2021, 22 : 1 - 34
  • [37] Radial Basis Function Networks with Optimal Kernels
    Krzyzak, Adam
    2011 IEEE INTERNATIONAL SYMPOSIUM ON INFORMATION THEORY PROCEEDINGS (ISIT), 2011, : 860 - 863
  • [38] Optimal Rates of Distributed Regression with Imperfect Kernels
    Sun, Hongwei
    Wu, Qiang
    JOURNAL OF MACHINE LEARNING RESEARCH, 2021, 22
  • [39] Graph kernels based on optimal node assignment
    Salim, Asif
    Shiju, S. S.
    Sumitra, S.
    KNOWLEDGE-BASED SYSTEMS, 2022, 244
  • [40] Gegenbauer polynomials, optimal kernels and Stancu operators
    Horova, I
    APPROXIMATION THEORY AND FUNCTION SERIES, 1996, 5 : 227 - 235
12345