凸序下Wasserstein投影的中心极限定理
Central limit theorem for Wasserstein projection - the case of convex order
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中文总结 AI 辅助
该研究建立了凸序下Wasserstein投影的中心极限定理，通过证明对偶可达性等性质，在温和矩假设下完成证明，还回答了Benjamin Jourdain的开放问题。
中文摘要 AI 辅助
本文主要聚焦于对推断任务有用的凸序下Wasserstein投影的极限定理，主要结果依赖于对偶可达性、稳定性及若干有用结论的建立。首先给出了调用经典代价函数c=h(x−y)上Wasserstein对偶性的清晰准则，引入了建立对偶可达性的新策略，证明了前后向对偶传输具有共轭关系，给出了确保最优对偶势唯一性的充分条件。这些要素为最优对偶势稳定性的证明奠定了基础，从而使我们能够在温和的矩假设下证明中心极限定理，进一步讨论表明该矩假设是最优的，这些结果还回答了Benjamin Jourdain教授提出的若干开放问题。
英文摘要
The main focuses of the article are limit theorems of Wasserstein projection in the convex order which are useful for inference tasks. The main results rely on the establishment of dual attainment, stability and several useful observations. The first is a clean criterion to invoke the Wasserstein projection dualities on the classical cost $c=h(x-y)$. A new strategy was introduced to establish the dual attainment. Backward and forward dual transport are proved to enjoy a conjugate relationship. Sufficient conditions are given that ensure uniqueness of the optimal dual potential. These ingredients laid the groundwork for the proof of optimal dual potential stability, thereby permitting us to prove the central limit theorems under mild moment assumptions. Additional discussions show that the moment assumptions are sharp. These results also answered several open questions raised by Professor Benjamin Jourdain.
发表机构
- Beihang University（北京航空航天大学）
机构由 AI 辅助整理，请以论文原文为准。
