In this work we consider regularized Wasserstein barycenters (average in Wasserstein distance) in Fourier basis. We prove that random Fourier parameters of the barycenter converge to some Gaussian random vector by distribution. The convergence rate has been derived in finite-sample case with explicit dependence on measures count ($n$) and the dimension of parameters ($p$).

翻译：在这项工作中,我们把正规化的瓦森斯坦(Wasserstein)百货中心(瓦森斯坦距离平均)放在Fourier的基础上。我们证明,该百货中心的随机Fourier参数通过分布方式与某些高西亚随机矢量相汇而成。 趋同率是在有限样本中得出的,明显依赖计量数($)和参数的维度($美元 ) 。