A New Robust Partial $p$-Wasserstein-Based Metric for Comparing Distributions

arXiv:2405.03664v1 Announce Type: new
Abstract: The $2$-Wasserstein distance is sensitive to minor geometric differences between distributions, making it a very powerful dissimilarity metric. However, due to this sensitivity, a small outlier mass can also cause a significant increase in the $2$-Wasserstein distance between two similar distributions. Similarly, sampling discrepancy can cause the empirical $2$-Wasserstein distance on $n$ samples in $\mathbb{R}^2$ to converge to the true distance at a rate of $n^{-1/4}$, which is significantly slower than the rate of $n^{-1/2}$ …

abstract arxiv cs.lg differences however making outlier robust sampling sensitivity small stat.ml type