论文标题
连续的正规化瓦斯坦barycenter
Continuous Regularized Wasserstein Barycenters
论文作者
论文摘要
Wasserstein Barycenter提供了一种基于最佳运输理论的概率分布的几何有意义的方法。在实践中，它们很难计算，但是，导致先前的工作将其支持限制为有限的积分。利用新的双重配方为正则化的Wasserstein Barycenter问题，我们引入了一种随机算法，该算法构建了Barycenter的连续近似。我们建立了强双重性，并使用相应的原始二元关系使用正规运输问题的双重电位隐式地对Barycenter进行参数化。可以通过随机梯度下降来解决最终的问题，该下降产生有效的在线算法，以近似给定样品访问的连续分布的重中心。我们证明了我们的方法的有效性，并与以前的合成示例和现实应用程序相比进行了比较。
Wasserstein barycenters provide a geometrically meaningful way to aggregate probability distributions, built on the theory of optimal transport. They are difficult to compute in practice, however, leading previous work to restrict their supports to finite sets of points. Leveraging a new dual formulation for the regularized Wasserstein barycenter problem, we introduce a stochastic algorithm that constructs a continuous approximation of the barycenter. We establish strong duality and use the corresponding primal-dual relationship to parametrize the barycenter implicitly using the dual potentials of regularized transport problems. The resulting problem can be solved with stochastic gradient descent, which yields an efficient online algorithm to approximate the barycenter of continuous distributions given sample access. We demonstrate the effectiveness of our approach and compare against previous work on synthetic examples and real-world applications.
