Related papers: Approximating 1-Wasserstein Distance with Trees
Optimal Transport has sparked vivid interest in recent years, in particular thanks to the Wasserstein distance, which provides a geometrically sensible and intuitive way of comparing probability measures. For computational reasons, the…
Wasserstein distances are increasingly used in a wide variety of applications in machine learning. Sliced Wasserstein distances form an important subclass which may be estimated efficiently through one-dimensional sorting operations. In…
Wasserstein distances are metrics on probability distributions inspired by the problem of optimal mass transportation. Roughly speaking, they measure the minimal effort required to reconfigure the probability mass of one distribution in…
Recent years have witnessed a tremendous growth using topological summaries, especially the persistence diagrams (encoding the so-called persistent homology) for analyzing complex shapes. Intuitively, persistent homology maps a potentially…
Distance measures between graphs are important primitives for a variety of learning tasks. In this work, we describe an unsupervised, optimal transport based approach to define a distance between graphs. Our idea is to derive…
Making sense of Wasserstein distances between discrete measures in high-dimensional settings remains a challenge. Recent work has advocated a two-step approach to improve robustness and facilitate the computation of optimal transport, using…
Sliced Wasserstein (SW) distances offer an efficient method for comparing high-dimensional probability measures by projecting them onto multiple 1-dimensional probability distributions. However, identifying informative slicing directions…
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…
Gromov-Wasserstein (GW) is a powerful tool to compare probability measures whose supports are in different metric spaces. GW suffers however from a computational drawback since it requires to solve a complex non-convex quadratic program. We…
The Wasserstein distance is a powerful metric based on the theory of optimal transport. It gives a natural measure of the distance between two distributions with a wide range of applications. In contrast to a number of the common…
We introduce the observable Wasserstein distance, a framework for deriving lower bounds on the Wasserstein distance between probability measures on Polish metric spaces, designed to bypass the computational intractability of exact optimal…
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…
We propose a methodology for intercomparing climate models and evaluating their performance against benchmarks based on the use of the Wasserstein distance (WD). This distance provides a rigorous way to measure quantitatively the difference…
In inverse problems, many conditional generative models approximate the posterior measure by minimizing a distance between the joint measure and its learned approximation. While this approach also controls the distance between the posterior…
Projection robust Wasserstein (PRW) distance, or Wasserstein projection pursuit (WPP), is a robust variant of the Wasserstein distance. Recent work suggests that this quantity is more robust than the standard Wasserstein distance, in…
Measuring similarities between different tasks is critical in a broad spectrum of machine learning problems, including transfer, multi-task, continual, and meta-learning. Most current approaches to measuring task similarities are…
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…
Uniform cost-distance Steiner trees minimize the sum of the total length and weighted path lengths from a dedicated root to the other terminals. They are applied when the tree is intended for signal transmission, e.g. in chip design or…
Comparing probability distributions is at the crux of many machine learning algorithms. Maximum Mean Discrepancies (MMD) and Wasserstein distances are two classes of distances between probability distributions that have attracted abundant…
The sliced-Wasserstein flow is an evolution equation where a probability density evolves in time, advected by a velocity field computed as the average among directions in the unit sphere of the optimal transport displacements from its 1D…