Related papers: Quasi Manhattan Wasserstein Distance
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…
We develop a kernel projected Wasserstein distance for the two-sample test, an essential building block in statistics and machine learning: given two sets of samples, to determine whether they are from the same distribution. This method…
We propose a generalization of the Wasserstein distance of order 1 to the quantum states of $n$ qudits. The proposal recovers the Hamming distance for the vectors of the canonical basis, and more generally the classical Wasserstein distance…
Quantifying the effect of noise on unitary operations is an essential task in quantum information processing. We propose the quantum Wasserstein distance between unitary operations, which shows an explanation for quantum circuit complexity…
The conventional sliced Wasserstein is defined between two probability measures that have realizations as vectors. When comparing two probability measures over images, practitioners first need to vectorize images and then project them to…
We consider several definitions of the quantum Wasserstein distance based on an optimization over general bipartite quantum states with given marginals. Then, we examine the quantities obtained after the optimization is carried out over…
Sliced Wasserstein (SW) distance suffers from redundant projections due to independent uniform random projecting directions. To partially overcome the issue, max K sliced Wasserstein (Max-K-SW) distance ($K\geq 1$), seeks the best…
Optimal transport has been very successful for various machine learning tasks; however, it is known to suffer from the curse of dimensionality. Hence, dimensionality reduction is desirable when applied to high-dimensional data with…
Self-supervised sequential recommendation significantly improves recommendation performance by maximizing mutual information with well-designed data augmentations. However, the mutual information estimation is based on the calculation of…
A generalization of the Wasserstein metric, the integrated transportation distance, establishes a novel distance between probability kernels of Markov systems. This metric serves as the foundation for an efficient approximation technique,…
Random probabilities are a key component to many nonparametric methods in Statistics and Machine Learning. To quantify comparisons between different laws of random probabilities several works are starting to use the elegant Wasserstein over…
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…
This paper uses sample data to study the problem of comparing populations on finite-dimensional parallelizable Riemannian manifolds and more general trivial vector bundles. Utilizing triviality, our framework represents populations as…
Computing the infinity Wasserstein distance and retrieving projections of a probability measure onto a closed subset of probability measures are critical sub-problems in various applied fields. However, the practical applicability of these…
Wasserstein GANs are based on the idea of minimising the Wasserstein distance between a real and a generated distribution. We provide an in-depth mathematical analysis of differences between the theoretical setup and the reality of training…
It is well known that the quadratic Wasserstein distance $W_2 (\mathord{\boldsymbol{\cdot}}, \mathord{\boldsymbol{\cdot}})$ is formally equivalent, for infinitesimally small perturbations, to some weighted $H^{-1}$ homogeneous Sobolev norm.…
Optimal transport provides a powerful mathematical framework with applications spanning numerous fields. A cornerstone within this domain is the $p$-Wasserstein distance, which serves to quantify the cost of transporting one probability…
Water and silicon are chemically dissimilar substances with common physical properties. Their liquids display a temperature of maximum density, increased diffusivity on compression, they form tetrahedral crystals and tetrahedral amorphous…
This paper considers the problem of regression over distributions, which is becoming increasingly important in machine learning. Existing approaches often ignore the geometry of the probability space or are computationally expensive. To…
Hilbert-Schmidt distance is one of the prominent distance measures in quantum information theory which finds applications in diverse problems, such as construction of entanglement witnesses, quantum algorithms in machine learning, and…