标题： 排列不变网络以学习Wasserstein度量 显示英文标题

标题： Permutation invariant networks to learn Wasserstein metrics

摘要： 理解在度量空间上配备Wasserstein距离的概率测度空间是数学分析中的基本问题之一。 Wasserstein度量在机器学习领域受到了广泛关注，特别是因为它比较分布的合理方式。 在本工作中，我们使用一个排列不变网络将概率测度的样本映射到低维空间，使得编码样本之间的欧几里得距离反映概率测度之间的Wasserstein距离。 我们证明了我们的网络可以推广以正确计算未见过的密度之间的距离。 我们还证明这些网络可以学习概率分布的一阶和二阶矩。 显示英文摘要

摘要： 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.