Related papers: Error Analysis of Triangular Optimal Transport Map…
Modeling traffic distribution and extracting optimal flows in multilayer networks is of utmost importance to design efficient multi-modal network infrastructures. Recent results based on optimal transport theory provide powerful and…
We study the optimal transport problem in the Euclidean space where the cost function is given by the value function associated with a Linear Quadratic minimization problem. Under appropriate assumptions, we generalize Brenier's Theorem…
We study the problem of causal structure learning from data using optimal transport (OT). Specifically, we first provide a constraint-based method which builds upon lower-triangular monotone parametric transport maps to design conditional…
We present a new approach to Bayesian inference that entirely avoids Markov chain simulation, by constructing a map that pushes forward the prior measure to the posterior measure. Existence and uniqueness of a suitable measure-preserving…
We demonstrate the relevance of an algorithm called generalized iterative scaling (GIS) or simultaneous multiplicative algebraic reconstruction technique (SMART) and its rescaled block-iterative version (RBI-SMART) in the field of optimal…
Motivated by optimal re-balancing of a portfolio, we formalize an optimal transport problem in which the transported mass is scaled by a mass-change factor depending on the source and destination. This allows direct modeling of the creation…
One of the central objects in the theory of optimal transport is the Brenier map: the unique monotone transformation which pushes forward an absolutely continuous probability law onto any other given law. A line of recent work has analyzed…
In the regime of bounded transportation costs, additive approximations for the optimal transport problem are reduced (rather simply) to relative approximations for positive linear programs, resulting in faster additive approximation…
Transportation of measure provides a versatile approach for modeling complex probability distributions, with applications in density estimation, Bayesian inference, generative modeling, and beyond. Monotone triangular transport…
We present a novel hierarchical framework for optimal transport (OT) using string diagrams, namely string diagrams of optimal transports. This framework reduces complex hierarchical OT problems to standard OT problems, allowing efficient…
Regularization by the Shannon entropy enables us to efficiently and approximately solve optimal transport problems on a finite set. This paper is concerned with regularized optimal transport problems via Bregman divergence. We introduce the…
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 many situations, simulation models are developed to handle complex real-world business optimisation problems. For example, a discrete-event simulation model is used to simulate the trailer management process in a big Fast-Moving Consumer…
Sampling conditional distributions is a fundamental task for Bayesian inference and density estimation. Generative models, such as normalizing flows and generative adversarial networks, characterize conditional distributions by learning a…
We present a flexible method for computing Bayesian optimal experimental designs (BOEDs) for inverse problems with intractable posteriors. The approach is applicable to a wide range of BOED problems and can accommodate various optimality…
This article reviews the use of first order convex optimization schemes to solve the discretized dynamic optimal transport problem, initially proposed by Benamou and Brenier. We develop a staggered grid discretization that is well adapted…
This paper presents a variational representation of the Bayes' law using optimal transportation theory. The variational representation is in terms of the optimal transportation between the joint distribution of the (state, observation) and…
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…
We study the Neural Optimal Transport (NOT) algorithm which uses the general optimal transport formulation and learns stochastic transport plans. We show that NOT with the weak quadratic cost might learn fake plans which are not optimal. To…
We study multi-marginal optimal transport problems from a probabilistic graphical model perspective. We point out an elegant connection between the two when the underlying cost for optimal transport allows a graph structure. In particular,…