论文标题
在自适应切成薄片的距离上散发出Pac-Bayesian灯
Shedding a PAC-Bayesian Light on Adaptive Sliced-Wasserstein Distances
论文作者
论文摘要
切成薄片的距离距离（SW）是一种计算高效且理论上接地的替代方案。然而，关于其统计特性的文献（或更准确地说，其概括性属性）在切片的分布（超出均匀度量之外）的分布是稀缺的。为了为这一研究带来新的贡献，我们利用Pac-bayesian理论和中心观察结果，即SW可以解释为平均风险，pac-bayesian界限的数量已设计为表征。我们提供了三种类型的结果：i）在我们称为自适应切片的距离距离上的豆豆泛化界限，即SW在切片的任意分布方面定义（其中包括数据依赖于数据的分布），ii）一种原则性的程序，以最大程度地分配我们的插图，以最大程度地分配我们的分布，以使我们的插图最大程度地分布，并赋予我们的inii II II II III范围。
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.
