为自适应切片-Wasserstein距离带来PAC-贝叶斯视角
Shedding a PAC-Bayesian Light on Adaptive Sliced-Wasserstein Distances
AI总结：
本文利用PAC-贝叶斯理论为自适应切片-Wasserstein距离建立泛化界，并提出通过优化理论界学习最具判别力的切片分布，辅以实验验证。
摘要：
切片-Wasserstein距离（SW）是Wasserstein距离的一种计算高效且具有理论基础的替代方案。然而，关于其统计性质——或更准确地说，其关于切片分布的泛化性质——的文献，在均匀测度之外的情形十分稀少。为了给这一研究方向带来新的贡献，我们利用PAC-贝叶斯理论以及一个核心观察：SW可以被解释为一种平均风险，而PAC-贝叶斯界正是为刻画这一量而设计的。我们提供三类结果：i）PAC-贝叶斯泛化界，适用于我们称之为自适应切片-Wasserstein距离的情形，即相对于任意切片分布（包括依赖于数据的分布）定义的SW；ii）一个有原则的程序，通过优化我们的理论界来学习能够产生最具判别力SW的切片分布；iii）对我们理论发现的实证说明。
英文摘要：
The Sliced-Wasserstein distance (SW) is a computationally efficient and theoretically grounded alternative to the Wasserstein distance. Yet, the literature on its statistical properties -- or, more accurately, its generalization properties -- with respect to the distribution of slices, beyond the uniform measure, is scarce. To bring new contributions to this line of research, we leverage the PAC-Bayesian theory and a central observation that SW may be interpreted as an average risk, the quantity PAC-Bayesian bounds have been designed to characterize. We provide three types of results: i) PAC-Bayesian generalization bounds that hold on what we refer as adaptive Sliced-Wasserstein distances, i.e. SW defined with respect to arbitrary distributions of slices (among which data-dependent distributions), ii) a principled procedure to learn the distribution of slices that yields maximally discriminative SW, by optimizing our theoretical bounds, and iii) empirical illustrations of our theoretical findings.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
