论文标题
固有切片的瓦斯坦距离，用于比较流形和图上的概率分布的集合
Intrinsic Sliced Wasserstein Distances for Comparing Collections of Probability Distributions on Manifolds and Graphs
论文作者
论文摘要
从用户活动模式分析到大脑连接组学的各种应用中，出现了概率分布的集合。在实践中，这些分布可以在不同的域类型上定义，包括有限间隔，圆圈，圆柱，球体，其他歧管和图形。本文介绍了一种检测两个分布集合之间在此类通用领域的差异的方法。为此，我们提出了固有的切片结构，该切片结构在歧管和图形上产生了一类新的Wasserstein距离。这些距离是希尔伯特（Hilbert）可嵌入的，使我们能够将分布收集比较问题减少到希尔伯特（Hilbert）空间中更熟悉的平均测试问题。我们提供两个基于重采样的测试程序，另一个基于合并坐标测试的p值的测试。我们在各种合成和真实数据设置中进行的实验表明，所得的测试功能强大，并且P值得到了良好的校准。
Collections of probability distributions arise in a variety of applications ranging from user activity pattern analysis to brain connectomics. In practice these distributions can be defined over diverse domain types including finite intervals, circles, cylinders, spheres, other manifolds, and graphs. This paper introduces an approach for detecting differences between two collections of distributions over such general domains. To this end, we propose the intrinsic slicing construction that yields a novel class of Wasserstein distances on manifolds and graphs. These distances are Hilbert embeddable, allowing us to reduce the distribution collection comparison problem to a more familiar mean testing problem in a Hilbert space. We provide two testing procedures one based on resampling and another on combining p-values from coordinate-wise tests. Our experiments in various synthetic and real data settings show that the resulting tests are powerful and the p-values are well-calibrated.
