论文标题
通过位移插值通过分布式Wasserstein Barycenters
Distributed Wasserstein Barycenters via Displacement Interpolation
论文作者
论文摘要
考虑一个多代理系统，每个代理都具有初始概率度量。在本文中，我们提出了一种基于随机，异步和成对的信息和位移插值的分布式算法。我们表征了该算法的演变，并证明它在各种条件下计算了初始度量的Wasserstein Barycenter。该算法的一个版本计算标准的瓦斯坦barycenter，即基于同等重量的barycenter；另一个版本计算了一个随机的瓦斯坦barycenter，即基于最初测量的随机权重的barycenter。最后，我们将算法专门用于高斯分布，并与数学社会学中意见动力学建模建立联系。
Consider a multi-agent system whereby each agent has an initial probability measure. In this paper, we propose a distributed algorithm based upon stochastic, asynchronous and pairwise exchange of information and displacement interpolation in the Wasserstein space. We characterize the evolution of this algorithm and prove it computes the Wasserstein barycenter of the initial measures under various conditions. One version of the algorithm computes a standard Wasserstein barycenter, i.e., a barycenter based upon equal weights; and the other version computes a randomized Wasserstein barycenter, i.e., a barycenter based upon random weights for the initial measures. Finally, we specialize our algorithm to Gaussian distributions and draw a connection with the modeling of opinion dynamics in mathematical sociology.
