相关论文: Wasserstein Style Transfer

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…

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…

The problem of modeling the relationship between univariate distributions and one or more explanatory variables has found increasing interest. Traditional functional data methods cannot be applied directly to distributional data because of…

The space of probability densities is an infinite-dimensional Riemannian manifold, with Riemannian metrics in two flavors: Wasserstein and Fisher--Rao. The former is pivotal in optimal mass transport (OMT), whereas the latter occurs in…

Image style transfer aims to manipulate the appearance of a source image, or "content" image, to share similar texture and colors of a target "style" image. Ideally, the style transfer manipulation should also preserve the semantic content…

We explore a robust version of the barycenter problem among $n$ centered Gaussian probability measures, termed Semi-Unbalanced Optimal Transport (SUOT)-based Barycenter, wherein the barycenter remains fixed while the others are relaxed…

Comparative visualization of scalar fields is often facilitated using similarity measures such as edit distances. In this paper, we describe a novel approach for similarity analysis of scalar fields that combines two recently introduced…

Wasserstein dictionary learning is an unsupervised approach to learning a collection of probability distributions that generate observed distributions as Wasserstein barycentric combinations. Existing methods for Wasserstein dictionary…

We discuss the relation between the Wasserstein distance of order 1 between probability distributions on a metric space, arising in the study of Monge-Kantorovich transport problem, and the spectral distance of noncommutative geometry.…

Multi-marginal optimal transport enables one to compare multiple probability measures, which increasingly finds application in multi-task learning problems. One practical limitation of multi-marginal transport is computational scalability…

We propose to send a Gaussian source over an average-power limited additive white Gaussian noise channel by transmitting a linear combination of the source sequence and the result of its quantization using a high dimensional Gaussian vector…

Computational implementation of optimal transport barycenters for a set of target probability measures requires a form of approximation, a widespread solution being empirical approximation of measures. We provide an $O(\sqrt{N/n})$…

We present a novel framework based on optimal transport for the challenging problem of comparing graphs. Specifically, we exploit the probabilistic distribution of smooth graph signals defined with respect to the graph topology. This allows…

This article details a novel numerical scheme to approximate gradient flows for optimal transport (i.e. Wasserstein) metrics. These flows have proved useful to tackle theoretically and numerically non-linear diffusion equations that model…

Gaussian Splatting (GS) has recently emerged as an efficient representation for rendering 3D scenes from 2D images and has been extended to images, videos, and dynamic 4D content. However, applying style transfer to GS-based…

Distributed consensus in the Wasserstein metric space of probability measures on the real line is introduced in this work. Convergence of each agent's measure to a common measure is proven under a weak network connectivity condition. The…

Generating samples given a specific label requires estimating conditional distributions. We derive a tractable upper bound of the Wasserstein distance between conditional distributions to lay the theoretical groundwork to learn conditional…

Style transfer aims to combine the content of one image with the artistic style of another. It was discovered that lower levels of convolutional networks captured style information, while higher levels captures content information. The…

We develop a notion of projections between sets of probability measures using the geometric properties of the 2-Wasserstein space. It is designed for general multivariate probability measures, is computationally efficient to implement, and…

A novel framework for density estimation under expectation constraints is proposed. The framework minimizes the Wasserstein distance between the estimated density and a prior, subject to the constraints that the expected value of a set of…