Wasserstein barycenters have become popular due to their ability to represent the average of probability measures in a geometrically meaningful way. In this paper, we present an algorithm to approximate the Wasserstein-2 barycenters of continuous measures via a generative model. Previous approaches rely on regularization (entropic/quadratic) which introduces bias or on input convex neural networks which are not expressive enough for large-scale tasks. In contrast, our algorithm does not introduce bias and allows using arbitrary neural networks. In addition, based on the celebrity faces dataset, we construct Ave, celeba! dataset which can be used for quantitative evaluation of barycenter algorithms by using standard metrics of generative models such as FID.
翻译:瓦塞斯坦中枢由于能够以几何意义的方式代表概率计量平均值而变得很受欢迎。 在本文中,我们提出了一个算法,通过基因模型将持续计量的瓦塞斯坦-2中枢近似于瓦塞斯坦-2中枢。以前的方法依赖于正规化(即有机/水藻),这种正规化导致偏见,或输入锥形神经网络,这些输入锥形神经网络不足以表达大规模任务。相反,我们的算法并不引入偏向,允许使用任意的神经网络。此外,根据名人脸数据集,我们构建了Ave, eleba!数据集,可以通过使用诸如FID等基因模型的标准指标,用于对中枢算法进行定量评估。