论文标题
Wasserstein距离的中心插入式估计
Centered plug-in estimation of Wasserstein distances
论文作者
论文摘要
平方Euclidean 2-Wasserstein距离的插入式估计器是保守的，但是由于其较大的正偏见通常是不明智的。我们使用基于线性组合的简单核心过程消除了大多数偏见。我们构建了一对中心的插件估计器，该估计器随着真正的Wasserstein距离而减小，因此，对于任何有限的样本量，可以保证具有信息。至关重要的是，我们证明这些估计量通常可以被视为平方瓦斯坦距离上的互补上限和下限。最后，我们将估计量应用于贝叶斯计算，开发用于估计的方法（i）近似推理方法的偏差以及（ii）MCMC算法的收敛。
The plug-in estimator of the squared Euclidean 2-Wasserstein distance is conservative, however due to its large positive bias it is often uninformative. We eliminate most of this bias using a simple centering procedure based on linear combinations. We construct a pair of centered plug-in estimators that decrease with the true Wasserstein distance, and are therefore guaranteed to be informative, for any finite sample size. Crucially, we demonstrate that these estimators can often be viewed as complementary upper and lower bounds on the squared Wasserstein distance. Finally, we apply the estimators to Bayesian computation, developing methods for estimating (i) the bias of approximate inference methods and (ii) the convergence of MCMC algorithms.
