Related papers: An Approximation Theory Framework for Measure-Tran…
We present a unified theoretical framework for parametric low-rank approximation, a research area devoted to the development of efficient algorithms that act as adaptive alternatives of traditional methods such as Singular Value…
We present a systematic analysis of estimation errors for a class of optimal transport based algorithms for filtering and data assimilation. Along the way, we extend previous error analyses of Brenier maps to the case of conditional Brenier…
We consider the rate-limited quantum-to-classical optimal transport in terms of output-constrained rate-distortion coding for both finite-dimensional and continuous-variable quantum-to-classical systems with limited classical common…
We consider the fundamental problem of sampling the optimal transport coupling between given source and target distributions. In certain cases, the optimal transport plan takes the form of a one-to-one mapping from the source support to the…
This article gives an introduction to optimal transport, a mathematical theory that makes it possible to measure distances between functions (or distances between more general objects), to interpolate between objects or to enforce…
Let $\pi_{0}$ and $\pi_{1}$ be two distributions on the Borel space $(\mathbb{R}^{d},\mathcal{B}(\mathbb{R}^{d}))$. Any measurable function $T:\mathbb{R}^{d}\rightarrow\mathbb{R}^{d}$ such that $Y=T(X)\sim\pi_{1}$ if $X\sim\pi_{0}$ is…
Optimal transport (OT) is a powerful tool for measuring the distance between two defined probability distributions. In this paper, we develop a new manifold named the coupling matrix manifold (CMM), where each point on CMM can be regarded…
We study fundamental theoretical aspects of probabilistic roadmaps (PRM) in the finite time (non-asymptotic) regime. In particular, we investigate how completeness and optimality guarantees of the approach are influenced by the underlying…
Porous and heterogeneous materials are found in many applications from composites, membranes, chemical reactors, and other engineered materials to biological matter and natural subsurface structures. In this work we propose an integrated…
Algorithms are now routinely used to make consequential decisions that affect human lives. Examples include college admissions, medical interventions or law enforcement. While algorithms empower us to harness all information hidden in vast…
Estimating the reachable set of a dynamical system is a fundamental problem in control theory, particularly when control inputs are bounded. Direct simulation using randomly sampled admissible controls often leads to trajectories that…
The aim of this paper is to obtain quantitative bounds for solutions to the optimal matching problem in dimension two. These bounds show that up to a logarithmically divergent shift, the optimal transport maps are close to be the identity…
Understanding human mobility is crucial for applications such as forecasting epidemic spreading, planning transport infrastructure and urbanism in general. While, traditionally, mobility information has been collected via surveys, the…
Optimal transport aims to estimate a transportation plan that minimizes a displacement cost. This is realized by optimizing the scalar product between the sought plan and the given cost, over the space of doubly stochastic matrices. When…
In the field of optimal transport, two prominent subfields face each other: (i) unregularized optimal transport, "\`a-la-Kantorovich", which leads to extremely sparse plans but with algorithms that scale poorly, and (ii)…
In many scientific fields imaging is used to relate a certain physical quantity to other dependent variables. Therefore, images can be considered as a map from a real-world coordinate system to the non-negative measurements being acquired.…
Many causal and structural parameters in economics can be identified and estimated by computing the value of an optimization program over all distributions consistent with the model and the data. Existing tools apply when the data is…
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.…
Brenier's theorem is a cornerstone of optimal transport that guarantees the existence of an optimal transport map $T$ between two probability distributions $P$ and $Q$ over $\mathbb{R}^d$ under certain regularity conditions. The main goal…
This paper presents a detailed theoretical analysis of the three stochastic approximation proximal gradient algorithms proposed in our companion paper [49] to set regularization parameters by marginal maximum likelihood estimation. We prove…