Related papers: Spherical Tree-Sliced Wasserstein Distance
The Gromov-Wasserstein (GW) problem provides a framework for aligning heterogeneous datasets by matching their intrinsic geometry, but its statistical and computational scaling remains an issue for high-dimensional problems. Slicing…
Anomaly detection (AD) has been an active research area in various domains. Yet, the increasing data scale, complexity, and dimension turn the traditional methods into challenging. Recently, the deep generative model, such as the…
Although optimal transport (OT) problems admit closed form solutions in a very few notable cases, e.g. in 1D or between Gaussians, these closed forms have proved extremely fecund for practitioners to define tools inspired from the OT…
Sliced Wasserstein distances preserve properties of classic Wasserstein distances while being more scalable for computation and estimation in high dimensions. The goal of this work is to quantify this scalability from three key aspects: (i)…
Optimal transport (OT) defines a powerful framework to compare probability distributions in a geometrically faithful way. However, the practical impact of OT is still limited because of its computational burden. We propose a new class of…
Multi-marginal optimal transport (MOT) is a generalization of optimal transport to multiple marginals. Optimal transport has evolved into an important tool in many machine learning applications, and its multi-marginal extension opens up for…
We propose min Generalized Sliced Gromov--Wasserstein (min-GSGW), a sliced formulation for the Gromov--Wasserstein (GW) problem using expressive generalized slicers. The key idea is to learn coupled nonlinear slicers that assign compatible…
Optimal transport is widely used to learn distributions, enforce distributional constraints, and model uncertainty. In applications, transport losses are often computed from samples through tractable representations, such as one-dimensional…
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…
There exist growing interests in intelligent systems for numerous medical imaging, image processing, and computer vision applications, such as face recognition, medical diagnosis, character recognition, and self-driving cars, among others.…
Regression loss design is an essential topic for oriented object detection. Due to the periodicity of the angle and the ambiguity of width and height definition, traditional L1-distance loss and its variants have been suffered from the…
Optimal Transport (OT) has established itself as a robust framework for quantifying differences between distributions, with applications that span fields such as machine learning, data science, and computer vision. This paper offers a…
We present the Fourier Sliced-Wasserstein (FSW) embedding - a novel method to embed multisets and measures over R^d into Euclidean space. Our proposed embedding approximately preserves the sliced Wasserstein distance on distributions,…
The power and flexibility of Optimal Transport (OT) have pervaded a wide spectrum of problems, including recent Machine Learning challenges such as unsupervised domain adaptation. Its essence of quantitatively relating two probability…
Discriminating between distributions is an important problem in a number of scientific fields. This motivated the introduction of Linear Optimal Transportation (LOT), which embeds the space of distributions into an $L^2$-space. The…
Estimating Wasserstein distances between two high-dimensional densities suffers from the curse of dimensionality: one needs an exponential (wrt dimension) number of samples to ensure that the distance between two empirical measures is…
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…
Relational regularized autoencoder (RAE) is a framework to learn the distribution of data by minimizing a reconstruction loss together with a relational regularization on the latent space. A recent attempt to reduce the inner discrepancy…
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…
Computing optimal transport (OT) distances such as the earth mover's distance is a fundamental problem in machine learning, statistics, and computer vision. In this paper, we study the problem of approximating the general OT distance…