Related papers: PT$\mathrm{L}^{p}$: Partial Transport $\mathrm{L}^…
We study the problem of estimating a function $T$ given independent samples from a distribution $P$ and from the pushforward distribution $T_\sharp P$. This setting is motivated by applications in the sciences, where $T$ represents the…
Optimal transport (OT) distances between probability distributions are parameterized by the ground metric they use between observations. Their relevance for real-life applications strongly hinges on whether that ground metric parameter is…
This paper aims at determining under which conditions the semi-discrete optimal transport is twice differentiable with respect to the parameters of the discrete measure and exhibits numerical applications. The discussion focuses on minimal…
Natural language processing (NLP) is a key component of intelligent transportation systems (ITS), but it faces many challenges in the transportation domain, such as domain-specific knowledge and data, and multi-modal inputs and outputs.…
Sliced Optimal Transport (SOT) is a rapidly developing branch of optimal transport (OT) that exploits the tractability of one-dimensional OT problems. By combining tools from OT, integral geometry, and computational statistics, SOT enables…
In this article, we define the transport dimension of probability measures on $\mathbb{R}^m$ using ramified optimal transportation theory. We show that the transport dimension of a probability measure is bounded above by the Minkowski…
We consider the optimal mass transportation problem in $\RR^d$ with measurably parameterized marginals, for general cost functions and under conditions ensuring the existence of a unique optimal transport map. We prove a joint measurability…
Optimal transport provides a robust framework for comparing probability distributions. Its effectiveness is significantly influenced by the choice of the underlying ground metric. Traditionally, the ground metric has either been (i)…
We propose a novel probabilistic approach to multilevel clustering problems based on composite transportation distance, which is a variant of transportation distance where the underlying metric is Kullback-Leibler divergence. Our method…
Given a $d$-dimensional continuous (resp. discrete) probability distribution $\mu$ and a discrete distribution $\nu$, the semi-discrete (resp. discrete) Optimal Transport (OT) problem asks for computing a minimum-cost plan to transport mass…
This paper presents a novel two-step approach for the fundamental problem of learning an optimal map from one distribution to another. First, we learn an optimal transport (OT) plan, which can be thought as a one-to-many map between the two…
Optimal transport (OT) naturally arises in a wide range of machine learning applications but may often become the computational bottleneck. Recently, one line of works propose to solve OT approximately by searching the \emph{transport plan}…
We introduce a new technique, which we call the boundary method, for solving semi-discrete optimal transport problems with a wide range of cost functions. The boundary method reduces the effective dimension of the problem, thus improving…
We bring a control perspective to the problem of identifying paths of measures for sampling via dynamic measure transport (DMT). We highlight the fact that commonly used paths may be poor choices for DMT and connect existing methods for…
Optimal transport distances have found many applications in machine learning for their capacity to compare non-parametric probability distributions. Yet their algorithmic complexity generally prevents their direct use on large scale…
In this work, we propose a novel method for quantifying distances between Toeplitz structured covariance matrices. By exploiting the spectral representation of Toeplitz matrices, the proposed distance measure is defined based on an optimal…
The use of distances based on optimal transportation has recently shown promise for discrimination of power spectra. In particular, spectral estimation methods based on l1 regularization as well as covariance based methods can be shown to…
In this paper, we tackle the inductive semi-supervised learning problem that aims to obtain label predictions for out-of-sample data. The proposed approach, called Optimal Transport Induction (OTI), extends efficiently an optimal transport…
One way to analyze complicated non-autonomous flows is through trying to understand their transport behavior. In a quantitative, set-oriented approach to transport and mixing, finite time coherent sets play an important role. These are…
For the basic case of $L_2$ optimal transport between two probability measures on a Euclidean space, the regularity of the coupling measure and the transport map in the tail regions of these measures is studied. For this purpose, Robert…