相关论文: Learning High Dimensional Wasserstein Geodesics

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…

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…

This paper introduces Wasserstein variational inference, a new form of approximate Bayesian inference based on optimal transport theory. Wasserstein variational inference uses a new family of divergences that includes both f-divergences and…

Optimal Transport has sparked vivid interest in recent years, in particular thanks to the Wasserstein distance, which provides a geometrically sensible and intuitive way of comparing probability measures. For computational reasons, the…

The Wasserstein distance is a metric on a space of probability measures that has seen a surge of applications in statistics, machine learning, and applied mathematics. However, statistical aspects of Wasserstein distances are bottlenecked…

Optimal transport provides an inherently geometric and highly structured framework for studying spaces of probability measures, supplying a rich theoretical toolkit for contemporary statistics, machine learning, and generative modelling. In…

We present a novel multiscale framework for analyzing sequences of probability measures in Wasserstein spaces over Euclidean domains. Exploiting the intrinsic geometry of optimal transport, we construct a multiscale transform applicable to…

Multiple marginal matching problem aims at learning mappings to match a source domain to multiple target domains and it has attracted great attention in many applications, such as multi-domain image translation. However, addressing this…

Optimal transport distances, otherwise known as Wasserstein distances, have recently drawn ample attention in computer vision and machine learning as a powerful discrepancy measure for probability distributions. The recent developments on…

We propose a fast algorithm for the calculation of the Wasserstein-1 distance, which is a particular type of optimal transport distance with homogeneous of degree one transport cost. Our algorithm is built on multilevel primal-dual…

Semi-discrete optimal transport problems, which evaluate the Wasserstein distance between a discrete and a generic (possibly non-discrete) probability measure, are believed to be computationally hard. Even though such problems are…

We propose a scalable robust learning algorithm combining kernel smoothing and robust optimization. Our method is motivated by the convex analysis perspective of distributionally robust optimization based on probability metrics, such as the…

We introduce a new approach for comparing reinforcement learning policies, using Wasserstein distances (WDs) in a newly defined latent behavioral space. We show that by utilizing the dual formulation of the WD, we can learn score functions…

We study optimization problems whereby the optimization variable is a probability measure. Since the probability space is not a vector space, many classical and powerful methods for optimization (e.g., gradients) are of little help. Thus,…

In this paper, we study the problem of learning compact (low-dimensional) representations for sequential data that captures its implicit spatio-temporal cues. To maximize extraction of such informative cues from the data, we set the problem…

We address the problem of efficiently computing Wasserstein distances for multiple pairs of distributions drawn from a meta-distribution. To this end, we propose a fast estimation method based on regressing Wasserstein distance on sliced…

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…

On the space of probability densities, we extend the Wasserstein geodesics to the case of higher-order interpolation such as cubic spline interpolation. After presenting the natural extension of cubic splines to the Wasserstein space, we…

We present new algorithms to compute the mean of a set of empirical probability measures under the optimal transport metric. This mean, known as the Wasserstein barycenter, is the measure that minimizes the sum of its Wasserstein distances…

Optimal transport distances (OT) have been widely used in recent work in Machine Learning as ways to compare probability distributions. These are costly to compute when the data lives in high dimension. Recent work by Paty et al., 2019,…