Related papers: Computing Wasserstein Distance for Persistence Dia…

Gaussian mixture models find their place as a powerful tool, mostly in the clustering problem, but with proper preparation also in feature extraction, pattern recognition, image segmentation and in general machine learning. When faced with…

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…

We prove an equivalence between open questions about the embeddability of the space of persistence diagrams and the space of probability distributions (i.e.~Wasserstein space). It is known that for many natural metrics, no coarse embedding…

Issued from Optimal Transport, the Wasserstein distance has gained importance in Machine Learning due to its appealing geometrical properties and the increasing availability of efficient approximations. In this work, we consider the problem…

An algorithm for approximating the p-Wasserstein distance between histograms defined on unstructured discrete grids is presented. It is based on the computation of a barycenter constrained to be supported on a low dimensional subspace,…

We study a class of quadratic Wasserstein distances on spaces consisting of generalized dynamical systems on a von Neumann algebra. We emphasize how symmetry of such a Wasserstein distance arises, but also study the asymmetric case. This…

The Quasi Manhattan Wasserstein Distance (QMWD) is a metric designed to quantify the dissimilarity between two matrices by combining elements of the Wasserstein Distance with specific transformations. It offers improved time and space…

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…

Despite of its importance for safe machine learning, uncertainty quantification for neural networks is far from being solved. State-of-the-art approaches to estimate neural uncertainties are often hybrid, combining parametric models with…

Quantum annealing is an optimization technique which potentially leverages quantum tunneling to enhance computational performance. Existing quantum annealers use superconducting flux qubits with short coherence times, limited primarily by…

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…

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…

We introduce a principled way of computing the Wasserstein distance between two distributions in a federated manner. Namely, we show how to estimate the Wasserstein distance between two samples stored and kept on different devices/clients…

Measuring the distance between ontological elements is fundamental for ontology matching. String-based distance metrics are notorious for shallow syntactic matching. In this exploratory study, we investigate Wasserstein distance targeting…

We investigate here the optimal transportation problem on configuration space for the quadratic cost. It is shown that, as usual, provided that the corresponding Wasserstein is finite, there exists one unique optimal measure and that this…

Wasserstein distances are widely used in modern data analysis but pose significant computational and statistical challenges in high dimensions. The sliced Wasserstein distance alleviates these challenges by leveraging one-dimensional…

Algebraic topology methods have recently played an important role for statistical analysis with complicated geometric structured data such as shapes, linked twist maps, and material data. Among them, \textit{persistent homology} is a…

In machine learning and particularly in topological data analysis, $\epsilon$-graphs are important tools but are generally hard to compute as the distance calculation between n points takes time O(n^2) classically. Recently, quantum…

Given a unitary transformation, what is the size of the smallest quantum circuit that implements it? This quantity, known as the quantum circuit complexity, is a fundamental property of quantum evolutions that has widespread applications in…

This paper presents a new approach to the classical problem of quantifying posterior contraction rates (PCRs) in Bayesian statistics. Our approach relies on Wasserstein distance, and it leads to two main contributions which improve on the…