Related papers: Multi-Dimensional Wasserstein Distance Implementat…
The Sliced Wasserstein (SW) distance has become a popular alternative to the Wasserstein distance for comparing probability measures. Widespread applications include image processing, domain adaptation and generative modelling, where it is…
We propose a fast algorithm for the calculation of the Wasserstein-1 distance, which is a particular type of optimal transport distance with homogeneous of degree one transport cost. Our algorithm is built on multilevel primal-dual…
The sliced Wasserstein metric compares probability measures on $\mathbb{R}^d$ by taking averages of the Wasserstein distances between projections of the measures to lines. The distance has found a range of applications in statistics and…
Many data clustering applications must handle objects that cannot be represented as vectors. In this context, the bag-of-vectors representation describes complex objects through discrete distributions, for which the Wasserstein distance…
We propose a new unsupervised anomaly detection method based on the sliced-Wasserstein distance for training data selection in machine learning approaches. Our filtering technique is interesting for decision-making pipelines deploying…
The transportation $\mathrm{L}^p$ distance, denoted $\mathrm{TL}^p$, has been proposed as a generalisation of Wasserstein $\mathrm{W}^p$ distances motivated by the property that it can be applied directly to colour or multi-channelled…
It was shown in [6] that the Wasserstein distance is equivalent to the Mean Optimal Sub-Pattern Assignment (MOSPA) measure for empirical probability density functions. A more recent paper [7], extends on it by drawing new connections…
Optimal transport is a foundational problem in optimization, that allows to compare probability distributions while taking into account geometric aspects. Its optimal objective value, the Wasserstein distance, provides an important loss…
We propose a fundamental metric for measuring the distance between two distributions. This metric, referred to as the decision-focused (DF) divergence, is tailored to stochastic linear optimization problems in which the objective…
Existing approaches to depth or disparity estimation output a distribution over a set of pre-defined discrete values. This leads to inaccurate results when the true depth or disparity does not match any of these values. The fact that this…
We define a modified Wasserstein distance for distribution clustering which inherits many of the properties of the Wasserstein distance but which can be estimated easily and computed quickly. The modified distance is the sum of two terms.…
The sliced Wasserstein (SW) distances between two probability measures are defined as the expectation of the Wasserstein distance between two one-dimensional projections of the two measures. The randomness comes from a projecting direction…
While the existing stochastic control theory is well equipped to handle dynamical systems with stochastic uncertainties, a paradigm shift using distance measure based decision making is required for the effective further exploration of the…
Sinkhorn divergence is a measure of dissimilarity between two probability measures. It is obtained through adding an entropic regularization term to Kantorovich's optimal transport problem and can hence be viewed as an entropically…
Causal optimal transport and adapted Wasserstein distance have applications in different fields from optimization to mathematical finance and machine learning. The goal of this article is to provide equivalent formulations of these concepts…
In this paper, we address the classification of instances each characterized not by a singular point, but by a distribution on a vector space. We employ the Wasserstein metric to measure distances between distributions, which are then used…
As a fundamental problem of natural language processing, it is important to measure the distance between different documents. Among the existing methods, the Word Mover's Distance (WMD) has shown remarkable success in document semantic…
In order to adapt the Wasserstein distance to the large sample multivariate non-parametric two-sample problem, making its application computationally feasible, permutation tests based on the Sinkhorn divergence between probability vectors…
This paper is a companion paper to [Lipman and Daubechies 2011]. We provide numerical procedures and algorithms for computing the alignment of and distance between two disk type surfaces. We provide a convergence analysis of the discrete…
Word embeddings are high dimensional vector representations of words that capture their semantic similarity in the vector space. There exist several algorithms for learning such embeddings both for a single language as well as for several…