论文标题
置换不变的网络以学习Wasserstein指标
Permutation invariant networks to learn Wasserstein metrics
论文作者
论文摘要
了解装有瓦斯坦距离的度量空间上的概率度量空间是数学分析中的基本问题之一。 Wasserstein指标在机器学习社区中受到了很多关注，尤其是其原则上的分布方式。在这项工作中，我们使用置换不变网络将样本从概率度量映射到一个低维空间中，以使编码样品之间的欧几里得距离反映了概率指标之间的沃斯坦斯坦距离。我们表明，我们的网络可以概括以正确计算看不见的密度之间的距离。我们还表明，这些网络可以学习概率分布的第一刻和第二刻。
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.
