论文标题
随机WASSERSTEIN BARYCENTER计算：统计保证的重新采样
Randomised Wasserstein Barycenter Computation: Resampling with Statistical Guarantees
论文作者
论文摘要
我们提出了一种混合重新采样方法，以近似大规模数据集上有限支持的Wasserstein Barycenters，可以将其与任何确切的求解器结合使用。在目标值的预期误差以及barycenter本身的预期误差上的非扰动界限允许校准计算成本和统计准确性。这些上限的速率被证明是最佳的，并且与仅在常数中出现的基础维度无关。使用Cuturi和Doucet的亚级别下降算法的简单修改，我们向无数的模拟数据集中展示了我们的方法的适用性，以及从细胞显微镜中提供的真实数据示例，这些示例无法触及ART算法在计算机上无法触及的计算算法。
We propose a hybrid resampling method to approximate finitely supported Wasserstein barycenters on large-scale datasets, which can be combined with any exact solver. Nonasymptotic bounds on the expected error of the objective value as well as the barycenters themselves allow to calibrate computational cost and statistical accuracy. The rate of these upper bounds is shown to be optimal and independent of the underlying dimension, which appears only in the constants. Using a simple modification of the subgradient descent algorithm of Cuturi and Doucet, we showcase the applicability of our method on a myriad of simulated datasets, as well as a real-data example from cell microscopy which are out of reach for state of the art algorithms for computing Wasserstein barycenters.
