发表机构
Yonsei University; Korea Institute for Advanced Study（延世大学; 韩国高等研究院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文通过最优传输理论严格推导对抗训练模型的中心极限定理，证明最优势唯一性，并给出鞍点稳定性与泛化误差的样本复杂度。
AI 中文摘要
本文旨在严格量化分类对抗训练模型的统计与学习理论性质。等价地，我们建立了经验最优部分传输的统计性质。具体而言，首先我们提供了两类中心极限定理（CLT）：以期望经验值为中心的CLT，以及以平滑后的总体值为中心的CLT。这些结果基于各种等价最优传输公式中最优势的唯一性，以及经验过程理论论证。对于二元情形，我们确实通过利用最优部分传输与推导出的多边际最优传输公式之间的联系，证明了最优势的唯一性。作为副产品，我们还获得了对抗训练模型鞍点的稳定性，以及泛化误差的样本复杂度和集中概率。
英文摘要
The purpose of this paper is to rigorously quantify the statistical and learning-theoretic properties of adversarial training models for classification. Equivalently, we establish the statistical properties of empirical optimal partial transport. Precisely, first we provide two types of central limit theorems (CLT): CLT centered at the expected empirical value, and CLT centered at the population one with smoothing. These results are based on the uniqueness of optimal potential for various equivalent optimal transport formulations, and the empirical process theory argument. For the binary setting, we indeed prove the uniqueness of optimal potential by leveraging the connection between optimal partial transport and the derived multi-marginal optimal transport formula. As byproducts, we also obtain the stability of a saddle point of the adversarial training model, and the sample complexity and concentration probability of the generalization error.
Comments49 pages, 1 figure; comments are welcome!
