相关论文: Parseval's Identity and Optimal Transport Maps
We determine the optimal structure of couplings for the \emph{Martingale transport problem} between radially symmetric initial and terminal laws $\mu, \nu$ on $\R^d$ and show the uniqueness of optimizer. Here optimality means that such…
We present an optimal mass transport framework on the space of Gaussian mixture models, which are widely used in statistical inference. Our method leads to a natural way to compare, interpolate and average Gaussian mixture models.…
In this paper, we propose a flow-based method for learning all-to-all transfer maps among conditional distributions that approximates pairwise optimal transport. The proposed method addresses the challenge of handling the case of continuous…
We present a systematic study of conditional triangular transport maps in function spaces from the perspective of optimal transportation and with a view towards amortized Bayesian inference. More specifically, we develop a theory of…
The basic optimal transportation problem consists in finding the most effective way of moving masses from one location to another, while minimizing the transportation cost. Such concept has been found to be useful to understand various…
We formulate and solve a class of finite-time transport and mixing problems in the set-oriented framework. The aim is to obtain optimal discrete-time perturbations in nonlinear dynamical systems to transport a specified initial measure on…
Continuity of the value of the martingale optimal transport problem on the real line w.r.t. its marginals was recently established in Backhoff-Veraguas and Pammer [2] and Wiesel [21]. We present a new perspective of this result using the…
Optimal transport has recently been brought forward as a tool for modeling and efficiently solving a variety of flow problems, such as origin-destination problems and multi-commodity flow problems. Although the framework has shown to be…
Optimal Transport (OT) theory investigates the cost-minimizing transport map that moves a source distribution to a target distribution. Recently, several approaches have emerged for learning the optimal transport map for a given cost…
Information geometry and optimal transport are two distinct geometric frameworks for modeling families of probability measures. During the recent years, there has been a surge of research endeavors that cut across these two areas and…
The basic problem of optimal transportation consists in minimizing the expected costs $\mathbb {E}[c(X_1,X_2)]$ by varying the joint distribution $(X_1,X_2)$ where the marginal distributions of the random variables $X_1$ and $X_2$ are…
The need to reason about uncertainty in large, complex, and multi-modal datasets has become increasingly common across modern scientific environments. The ability to transform samples from one distribution $P$ to another distribution $Q$…
We present a neural framework for learning conditional optimal transport (OT) maps between probability distributions. Our approach introduces a conditioning mechanism capable of processing both categorical and continuous conditioning…
Semidiscrete optimal transport is a challenging generalization of the classical transportation problem in linear programming. The goal is to design a joint distribution for two random variables (one continuous, one discrete) with fixed…
The main result of this paper is the existence of an optimal transport map $T$ between two given measures $\mu$ and $\nu$, for a cost which considers the maximal oscillation of $T$ at scale $\delta$, given by…
Recently, Optimal Transport has been proposed as a probabilistic framework in Machine Learning for comparing and manipulating probability distributions. This is rooted in its rich history and theory, and has offered new solutions to…
We study in this paper optimal mass transport over a strongly connected, directed graph on a given discrete time interval. Differently from previous literature, we do not assume full knowledge of the initial and final goods distribution…
We consider the transfer operators of non-uniformly expanding maps for potentials of various regularity, and show that a specific property of potentials ("flatness") implies a Ruelle-Perron-Frobenius Theorem and a decay of the transfer…
This paper is devoted to variational problems on the set of probability measures which involve optimal transport between unequal dimensional spaces. In particular, we study the minimization of a functional consisting of the sum of a term…
Optimal Transport has recently gained interest in machine learning for applications ranging from domain adaptation, sentence similarities to deep learning. Yet, its ability to capture frequently occurring structure beyond the "ground…