Scalable Computations of Wasserstein Barycenter via Input Convex Neural Networks
Scalable Computations of Wasserstein Barycenter via Input Convex Neural Networks
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发表时间：
2020-07
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通讯作者：
JiaoJiao Fan;A. Taghvaei;Yongxin Chen
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作者：
JiaoJiao Fan;A. Taghvaei;Yongxin Chen
Wasserstein Barycenter 是一种利用最佳传输诱导的几何结构来表示给定概率分布集的加权平均值的原则方法。在这项工作中，我们提出了一种新颖的可扩展算法来近似 Wasserstein 重心，旨在机器学习中的高维应用。我们提出的算法基于 2-Wasserstein 距离的 Kantorovich 对偶公式以及最近的神经网络架构，即输入凸神经网络，已知该网络可以参数化凸函数。我们的方法的显着特征是：i）它只需要来自边际分布的样本； ii）与现有的半离散方法不同，它用生成模型表示重心； iii) 它允许在一次训练后计算任意权重的重心。我们通过在多个实验中将其与最先进的方法进行比较来证明我们的算法的有效性。
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 2-Wasserstein 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 semi-discrete approaches, it represents the Barycenter with a generative model; iii) it allows to compute the barycenter with arbitrary weights after one training session. We demonstrate the efficacy of our algorithm by comparing it with the state-of-art methods in multiple experiments.