论文标题
稳定性和上限，用于统计不平衡运输电位的统计估算
Stability and upper bounds for statistical estimation of unbalanced transport potentials
论文作者
论文摘要
在本说明中，我们以二次成本的不平衡最佳运输（UOT）地图的统计估计率得出了上限。我们的工作依赖于将最佳运输（OT）半偶尔配方的稳定性扩展到不平衡的情况下。根据所考虑的UOT变体，我们的稳定性结果在OT（平衡）情况之间进行了插值，在OT（平衡）情况下，对于Sobolev Semi-Norm H1点仅在局部强烈凸出，并且相对于H 1标准，它在局部局部强烈凸。当最佳电位属于具有足够低度量的特定级别C时，局部强凸度使我们能够恢复超过1 / root n的超级参数率。
In this note, we derive upper-bounds on the statistical estimation rates of unbalanced optimal transport (UOT) maps for the quadratic cost. Our work relies on the stability of the semi-dual formulation of optimal transport (OT) extended to the unbalanced case. Depending on the considered variant of UOT, our stability result interpolates between the OT (balanced) case where the semi-dual is only locally strongly convex with respect the Sobolev semi-norm H1 dot and the case where it is locally strongly convex with respect to the H 1 norm. When the optimal potential belongs to a certain class C with sufficiently low metric-entropy, local strong convexity enables us to recover super-parametric rates, faster than 1 / root n.
