Related papers: Distance-Based Tree-Sliced Wasserstein Distance
Optimal Transport (OT) offers a powerful framework for finding correspondences between distributions and addressing matching and alignment problems in various areas of computer vision, including shape analysis, image generation, and…
In this paper, we consider the problem of computing the integral of a function on the unit sphere, in any dimension, using Monte Carlo methods. Although the methods we present are general, our guiding thread is the sliced Wasserstein…
Gromov-Wasserstein distances are generalization of Wasserstein distances, which are invariant under distance preserving transformations. Although a simplified version of optimal transport in Wasserstein spaces, called linear optimal…
Decision tree (DT) attracts persistent research attention due to its impressive empirical performance and interpretability in numerous applications. However, the growth of traditional yet widely-used univariate decision trees (UDTs) is…
Mesh deformation plays a pivotal role in many 3D vision tasks including dynamic simulations, rendering, and reconstruction. However, defining an efficient discrepancy between predicted and target meshes remains an open problem. A prevalent…
The Sliced-Wasserstein (SW) distance between probability measures is defined as the average of the Wasserstein distances resulting for the associated one-dimensional projections. As a consequence, the SW distance can be written as an…
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…
Wasserstein distance is a key metric for quantifying data divergence from a distributional perspective. However, its application in privacy-sensitive environments, where direct sharing of raw data is prohibited, presents significant…
The problem of comparing probability distributions is at the heart of many tasks in statistics and machine learning. Established comparison methods treat the standard setting that the distributions are supported in the same space. Recently,…
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…
Computing optimal transport (OT) between measures in high dimensions is doomed by the curse of dimensionality. A popular approach to avoid this curse is to project input measures on lower-dimensional subspaces (1D lines in the case of…
The Radon cumulative distribution transform (R-CDT) exploits one-dimensional Wasserstein transport and the Radon transform to represent prominent features in images. It is closely related to the sliced Wasserstein distance and facilitates…
We propose a novel Wasserstein method with a distillation mechanism, yielding joint learning of word embeddings and topics. The proposed method is based on the fact that the Euclidean distance between word embeddings may be employed as the…
We present a framework for embedding graph structured data into a vector space, taking into account node features and topology of a graph into the optimal transport (OT) problem. Then we propose a novel distance between two graphs, named…
The sliced Wasserstein distance as well as its variants have been widely considered in comparing probability measures defined on $\mathbb R^d$. Here we derive the notion of sliced Wasserstein distance for measures on an infinite dimensional…
Motivated by the growing popularity of variants of the Wasserstein distance in statistics and machine learning, we study statistical inference for the Sliced Wasserstein distance--an easily computable variant of the Wasserstein distance.…
This paper presents a generalization of the Wasserstein distance for both persistence diagrams and merge trees [20], [66] that takes advantage of the regions of their topological features in the input domain. Specifically, we redefine the…
Collections of probability distributions arise in a variety of applications ranging from user activity pattern analysis to brain connectomics. In practice these distributions can be defined over diverse domain types including finite…
Distributionally robust supervised learning (DRSL) is emerging as a key paradigm for building reliable machine learning systems for real-world applications -- reflecting the need for classifiers and predictive models that are robust to the…
The ubiquity of sequences in many domains enhances significant recent interest in sequence learning, for which a basic problem is how to measure the distance between sequences. Dynamic time warping (DTW) aligns two sequences by nonlinear…