6 accepted papers
The sensitivity of optimal transport (OT) to noise has motivated the study of robust variants. In this paper, we study two such formulations of semi-discrete OT in $\mathbb{R}^d$: (i) the $\alpha$-optimal partial transport, which minimizes the cost of transporting a mass of $\alpha$; and (ii) the $\…
The $p$-Wasserstein distance measures the cost of optimally transporting one distribution to another, where the cost of moving a unit mass from $a$ to $b$ is the $p^{th}$ power of the ground distance $\mathrm{d}(a,b)$ between them. Despite its strong theoretical properties, its use in practice --…
Optimal Transport (OT, also known as the Wasserstein distance) is a popular metric for comparing probability distributions and has been successfully used in many machine-learning applications. In the semi-discrete $2$-Wasserstein problem, we wish to compute the cheapest way to transport all the mass…
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 distributio…
We consider the problem of computing the $1$-Wasserstein distance $\mathcal{W}(\mu,\nu)$ between two $d$-dimensional discrete distributions $\mu$ and $\nu$ whose support lie within the unit hypercube. There are several algorithms that estimate $\mathcal{W}(\mu,\nu)$ within an additive error of $\var…
Algorithms for the minimum-cost bipartite matching can be used to estimate Wasserstein distance between two distributions. Given two sets $A$ and $B$ of $n$ points in a $2$-dimensional Euclidean space, one can use a fast implementation of the Hungarian method to compute a minimum-cost bipartite matc…