Related papers: On The Chain Rule Optimal Transport Distance
The use of optimal transport cost for learning generative models has become popular with Wasserstein Generative Adversarial Networks (WGAN). Training of WGAN relies on a theoretical background: the calculation of the gradient of the optimal…
Optimal Transport (OT) has recently emerged as a powerful framework for learning minimal-displacement maps between distributions. The predominant approach involves a neural parametrization of the Monge formulation of OT, typically assuming…
We consider the problem of solving the optimal transport problem between two empirical distributions with missing values. Our main assumption is that the data is missing completely at random (MCAR), but we allow for heterogeneous…
Comparing metric measure spaces (i.e. a metric space endowed with aprobability distribution) is at the heart of many machine learning problems. The most popular distance between such metric measure spaces is theGromov-Wasserstein (GW)…
In this paper, we introduce a variant of optimal transport adapted to the causal structure given by an underlying directed graph $G$. Different graph structures lead to different specifications of the optimal transport problem. For…
The optimal transport (OT) problem is a classical optimization problem having the form of linear programming. Machine learning applications put forward new computational challenges in its solution. In particular, the OT problem defines a…
Personalized recommender systems are playing an increasingly important role as more content and services become available and users struggle to identify what might interest them. Although matrix factorization and deep learning based methods…
In this paper, we study the problem of learning one-dimensional Gaussian mixture models (GMMs) with a specific focus on estimating both the model order and the mixing distribution from independent and identically distributed (i.i.d.)…
The Wasserstein distance between mixing measures has come to occupy a central place in the statistical analysis of mixture models. This work proposes a new canonical interpretation of this distance and provides tools to perform inference on…
We study a class of dynamically consistent risk measures that robustify a time-homogeneous Markovian reference model by allowing for distributional uncertainty in its transition laws. We start from one-step convex risk evaluations in which…
We study distributionally robust optimization with Sinkhorn distance -- a variant of Wasserstein distance based on entropic regularization. We derive a convex programming dual reformulation for general nominal distributions, transport…
Optimal mass transport, also known as the earth mover's problem, is an optimization problem with important applications in various disciplines, including economics, probability theory, fluid dynamics, cosmology and geophysics to cite a few.…
We derive distributional limits for empirical transport distances between probability measures supported on countable sets. Our approach is based on sensitivity analysis of optimal values of infinite dimensional mathematical programs and a…
Particle-based variational inference offers a flexible way of approximating complex posterior distributions with a set of particles. In this paper we introduce a new particle-based variational inference method based on the theory of…
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…
We study a variant of the dynamical optimal transport problem in which the energy to be minimised is modulated by the covariance matrix of the distribution. Such transport metrics arise naturally in mean-field limits of certain ensemble…
In machine learning and computer vision, optimal transport has had significant success in learning generative models and defining metric distances between structured and stochastic data objects, that can be cast as probability measures. The…
The mathematical forces at work behind Generative Adversarial Networks raise challenging theoretical issues. Motivated by the important question of characterizing the geometrical properties of the generated distributions, we provide a…
Inspired by the Kantorovich formulation of optimal transport distance between probability measures on a metric space, Gromov-Wasserstein (GW) distances comprise a family of metrics on the space of isomorphism classes of metric measure…
Distributionally-robust optimization is often studied for a fixed set of distributions rather than time-varying distributions that can drift significantly over time (which is, for instance, the case in finance and sociology due to…