Related papers: Quantization-based Bounds on the Wasserstein Metri…
We consider stochastic programs where the distribution of the uncertain parameters is only observable through a finite training dataset. Using the Wasserstein metric, we construct a ball in the space of (multivariate and non-discrete)…
Mutual information maximization has emerged as a powerful learning objective for unsupervised representation learning obtaining state-of-the-art performance in applications such as object recognition, speech recognition, and reinforcement…
Assume that we observe i.i.d.~points lying close to some unknown $d$-dimensional $\mathcal{C}^k$ submanifold $M$ in a possibly high-dimensional space. We study the problem of reconstructing the probability distribution generating the…
We study the Wasserstein natural gradient in parametric statistical models with continuous sample spaces. Our approach is to pull back the $L^2$-Wasserstein metric tensor in the probability density space to a parameter space, equipping the…
We consider a general task called partial Wasserstein covering with the goal of providing information on what patterns are not being taken into account in a dataset (e.g., dataset used during development) compared with another dataset(e.g.,…
The challenge of approximating functions in infinite-dimensional spaces from finite samples is widely regarded as formidable. We delve into the challenging problem of the numerical approximation of Sobolev-smooth functions defined on…
Optimal transport (OT) is a popular tool in machine learning to compare probability measures geometrically, but it comes with substantial computational burden. Linear programming algorithms for computing OT distances scale cubically in the…
We address the estimation problem for general finite mixture models, with a particular focus on the elliptical mixture models (EMMs). Compared to the widely adopted Kullback-Leibler divergence, we show that the Wasserstein distance provides…
We study discretizations of Hamiltonian systems on the probability density manifold equipped with the $L^2$-Wasserstein metric. Based on discrete optimal transport theory, several Hamiltonian systems on graph (lattice) with different…
This work deals with a class of one-dimensional measure-valued kinetic equations, which constitute extensions of the Kac caricature. It is known that if the initial datum belongs to the domain of normal attraction of an \alpha-stable law,…
Wasserstein barycenters define averages of probability measures in a geometrically meaningful way. Their use is increasingly popular in applied fields, such as image, geometry or language processing. In these fields however, the probability…
In this thesis, we consider the Wasserstein barycenter problem of discrete probability measures from computational and statistical sides. The statistical focus is estimating the sample size of measures necessary to calculate an…
Algorithmic stability is an important notion that has proven powerful for deriving generalization bounds for practical algorithms. The last decade has witnessed an increasing number of stability bounds for different algorithms applied on…
Compressing large Neural Networks (NN) by quantizing the parameters, while maintaining the performance is highly desirable due to reduced memory and time complexity. In this work, we cast NN quantization as a discrete labelling problem, and…
This paper provides a simple procedure to fit generative networks to target distributions, with the goal of a small Wasserstein distance (or other optimal transport costs). The approach is based on two principles: (a) if the source…
We present a framework for obtaining explicit bounds on the rate of convergence to equilibrium of a Markov chain on a general state space, with respect to both total variation and Wasserstein distances. For Wasserstein bounds, our main tool…
Wasserstein barycentres represent average distributions between multiple probability measures for the Wasserstein distance. The numerical computation of Wasserstein barycentres is notoriously challenging. A common approach is to use…
Optimal transport provides a powerful mathematical framework with applications spanning numerous fields. A cornerstone within this domain is the $p$-Wasserstein distance, which serves to quantify the cost of transporting one probability…
Optimal transport (OT)-based methods have a wide range of applications and have attracted a tremendous amount of attention in recent years. However, most of the computational approaches of OT do not learn the underlying transport map.…
Computing the empirical Wasserstein distance in the Wasserstein-distance-based independence test is an optimal transport (OT) problem with a special structure. This observation inspires us to study a special type of OT problem and propose a…