学习瓦塞斯坦指标的变异性网络 (Permutation invariant networks to learn Wasserstein metrics)

from arxiv, Fix typos, Accepted as a spotlight at Topological Data Analysis and Beyond Workshop at Neurips 2020. Added more experiments and results. Comments welcome

Understanding the space of probability measures on a metric space equipped with a Wasserstein distance is one of the fundamental questions in mathematical analysis. The Wasserstein metric has received a lot of attention in the machine learning community especially for its principled way of comparing distributions. In this work, we use a permutation invariant network to map samples from probability measures into a low-dimensional space such that the Euclidean distance between the encoded samples reflects the Wasserstein distance between probability measures. We show that our network can generalize to correctly compute distances between unseen densities. We also show that these networks can learn the first and the second moments of probability distributions.

翻译：在数学分析中,数学分析的根本问题之一是了解具有瓦塞斯坦距离的计量空间的概率空间。瓦塞斯坦指标在机器学习界受到了很多关注,特别是因为它有原则地比较分布分布。在这项工作中,我们使用一个变异网络将样本从概率测量到低维空间的图象绘制成图,使编码样本之间的欧立德距离反映瓦塞斯坦距离的概率测量。我们表明我们的网络可以概括地正确计算未知密度之间的距离。我们还表明,这些网络可以了解概率分布的第一和第二时刻。