论文标题
通过输入凸神经网络对Wasserstein Barycenter的可扩展计算
Scalable Computations of Wasserstein Barycenter via Input Convex Neural Networks
论文作者
论文摘要
Wasserstein Barycenter是一种原则上的方法，可以使用由最佳运输诱导的几何形状来表示给定的一组概率分布的加权平均值。在这项工作中，我们提出了一种新型的可扩展算法，以近似旨在用于机器学习中高度应用的Wasserstein Barycenters。我们提出的算法基于Wasserstein-2距离的Kantorovich双重公式以及最新的神经网络结构，即输入凸神经网络，这是已知可以参数化凸函数的。我们方法的区别特征是：i）仅需要边际分布中的样本； ii）与现有方法不同，它代表带有生成模型的重中心，因此可以在不查询边缘分布的情况下从重中心产生无限的样品； iii）在一个边际情况下，它的作用类似于生成对抗模型。我们通过将算法与多个实验中的最新方法进行比较来证明算法的疗效。
Wasserstein Barycenter is a principled approach to represent the weighted mean of a given set of probability distributions, utilizing the geometry induced by optimal transport. In this work, we present a novel scalable algorithm to approximate the Wasserstein Barycenters aiming at high-dimensional applications in machine learning. Our proposed algorithm is based on the Kantorovich dual formulation of the Wasserstein-2 distance as well as a recent neural network architecture, input convex neural network, that is known to parametrize convex functions. The distinguishing features of our method are: i) it only requires samples from the marginal distributions; ii) unlike the existing approaches, it represents the Barycenter with a generative model and can thus generate infinite samples from the barycenter without querying the marginal distributions; iii) it works similar to Generative Adversarial Model in one marginal case. We demonstrate the efficacy of our algorithm by comparing it with the state-of-art methods in multiple experiments.
