论文标题
一种基于GPM的算法，用于在某些概率度量的空间中解决正则化的Wasserstein Barycenter问题
A GPM-based algorithm for solving regularized Wasserstein barycenter problems in some spaces of probability measures
论文作者
论文摘要
在本文中，我们专注于对正规化的瓦斯坦barycenter问题的分析。我们为两种重要类别的概率措施提供了唯一性和barycenter的特征：（i）高斯分布和（ii）$ q $ - 高斯分布；每个由特定的熵功能正规。我们提出了一种基于矩阵空间中梯度投影方法的算法，以计算这些正则化的重中心。我们还考虑了一般类别的$φ$ - 指数度量，仅研究非注册的重中心。最后，我们从数值上显示了参数的影响和算法的稳定性，在数据的小扰动下。
In this paper, we focus on the analysis of the regularized Wasserstein barycenter problem. We provide uniqueness and a characterization of the barycenter for two important classes of probability measures: (i) Gaussian distributions and (ii) $q$-Gaussian distributions; each regularized by a particular entropy functional. We propose an algorithm based on gradient projection method in the space of matrices in order to compute these regularized barycenters. We also consider a general class of $φ$-exponential measures, for which only the non-regularized barycenter is studied. Finally, we numerically show the influence of parameters and stability of the algorithm under small perturbation of data.
