相关论文: Gromov-Wasserstein Distances: Entropic Regularizat…
We study a general formulation of regularized Wasserstein barycenters that enjoys favorable regularity, approximation, stability and (grid-free) optimization properties. This barycenter is defined as the unique probability measure that…
Gaussian mixture distributions are commonly employed to represent general probability distributions. Despite the importance of using Gaussian mixtures for uncertainty estimation, the entropy of a Gaussian mixture cannot be calculated…
We develop a full theory for the new class of Optimal Entropy-Transport problems between nonnegative and finite Radon measures in general topological spaces. They arise quite naturally by relaxing the marginal constraints typical of Optimal…
Generative Adversarial Networks (GANs) are one of the most practical methods for learning data distributions. A popular GAN formulation is based on the use of Wasserstein distance as a metric between probability distributions.…
Optimal transport (OT) based data analysis is often faced with the issue that the underlying cost function is (partially) unknown. This paper is concerned with the derivation of distributional limits for the empirical OT value when the cost…
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…
This paper explores the problem of generative modeling, aiming to simulate diverse examples from an unknown distribution based on observed examples. While recent studies have focused on quantifying the statistical precision of popular…
Dynamic Time Warping (DTW) and Geometric Edit Distance (GED) are basic similarity measures between curves or general temporal sequences (e.g., time series) that are represented as sequences of points in some metric space $(X,…
Optimal Transport has received much attention in Machine Learning as it allows to compare probability distributions by exploiting the geometry of the underlying space. However, in its original formulation, solving this problem suffers from…
The Wasserstein metric has become increasingly important in many machine learning applications such as generative modeling, image retrieval and domain adaptation. Despite its appeal, it is often too costly to compute. This has motivated…
The ratio between the gravitational waves (GW) and electromagnetic waves (EMW) luminosity distance ratio is a key observable that allows to test the nature of gravity, using gravitational waves emitted from compact binary coalescences. We…
Wasserstein Generative Adversarial Networks (WGANs) are the popular generative models built on the theory of Optimal Transport (OT) and the Kantorovich duality. Despite the success of WGANs, it is still unclear how well the underlying OT…
In this paper, we aim to provide a statistical theory for object matching based on the Gromov-Wasserstein distance. To this end, we model general objects as metric measure spaces. Based on this, we propose a simple and efficiently…
This work investigates several aspects related to quantitative stability in optimal transport, as well as uniqueness of the dual transport problem. Our main contributions are as follows. Chapter 1: Observations regarding the quantitative…
We provide a framework to approximate the 2-Wasserstein distance and the optimal transport map, amenable to efficient training as well as statistical and geometric analysis. With the quadratic cost and considering the Kantorovich dual form…
Replacing positivity constraints by an entropy barrier is popular to approximate solutions of linear programs. In the special case of the optimal transport problem, this technique dates back to the early work of Schr\"odinger. This approach…
Obtaining solutions to Optimal Transportation (OT) problems is typically intractable when the marginal spaces are continuous. Recent research has focused on approximating continuous solutions with discretization methods based on i.i.d.…
Optimal transport is widely used in pure and applied mathematics to find probabilistic solutions to hard combinatorial matching problems. We extend the Wasserstein metric and other elements of optimal transport from the matching of sets to…
This paper establishes the quantitative stability of invariant measures $\mu_{\alpha}$ for $\mathbb{R}^d$-valued ergodic stochastic differential equations driven by rotationally invariant multiplicative $\alpha$-stable processes with…
This note addresses computational difficulty of the Gromov-Wasserstein distance frequently mentioned in the literature. We provide details on the structure of the Gromov-Wasserstein distance optimization problem that show its non-convex…