Related papers: Optimal Transport of Information
We study an information design problem with continuous state and discrete signal space. Under convex and S-shaped value functions, the optimal information structure is interval-partitional and exhibits a dual expectations property: each…
Models of many real-life applications, such as queuing models of communication networks or computing systems, have a countably infinite state-space. Algorithmic and learning procedures that have been developed to produce optimal policies…
Recent advances in large-scale optimal transport have greatly extended its application scenarios in machine learning. However, existing methods either not explicitly learn the transport map or do not support general cost function. In this…
We rephrase Monge's optimal transportation (OT) problem with quadratic cost--via a Monge-Amp\`ere equation--as an infinite-dimensional optimization problem, which is in fact a convex problem when the target is a log-concave measure with…
An optimal transport problem on finite spaces is a linear program. Recently, a relaxation of the optimal transport problem via strictly convex functions, especially via the Kullback--Leibler divergence, sheds new light on data sciences.…
Optimal transport aligns samples across distributions by minimizing the transportation cost between them, e.g., the geometric distances. Yet, it ignores coherence structure in the data such as clusters, does not handle outliers well, and…
Persuasion studies how an informed principal may influence the behavior of agents by the strategic provision of payoff-relevant information. We focus on the fundamental multi-receiver model by Arieli and Babichenko (2019), in which there…
In this paper, we present a novel and principled approach to learn the optimal transport between two distributions, from samples. Guided by the optimal transport theory, we learn the optimal Kantorovich potential which induces the optimal…
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…
In many real world problems, optimization decisions have to be made with limited information. The decision maker may have no a priori or posteriori data about the often nonconvex objective function except from on a limited number of points…
The inverse optimal transport problem is to find the underlying cost function from the knowledge of optimal transport plans. While this amounts to solving a linear inverse problem, in this work we will be concerned with the nonlinear…
In this paper we propose a Bayesian, information theoretic approach to dimensionality reduction. The approach is formulated as a variational principle on mutual information, and seamlessly addresses the notions of sufficiency, relevance,…
Bayesian optimal sensor placement, in its full generality, seeks to maximize the mutual information between uncertain model parameters and the predicted data to be collected from the sensors for the purpose of performing Bayesian inference.…
We consider Monge-Kantorovich optimal transport problems on $\mathbb{R}^d$, $d\ge 1$, with a convex cost function given by the cumulant generating function of a probability measure. Examples include the Wasserstein-2 transport whose cost…
Traffic navigation services have gained widespread adoption in recent years. The route recommendations generated by these services often leads to severe congestion on urban streets, raising concerns from neighboring residents and city…
Optimal dimensionality reduction methods are proposed for the Bayesian inference of a Gaussian linear model with additive noise in presence of overabundant data. Three different optimal projections of the observations are proposed based on…
A sender persuades a strategically naive decisionmaker (DM) by committing privately to an experiment. Sender's choice of experiment is unknown to the DM, who must form her posterior beliefs nonparametrically by applying some learning rule…
A novel methodology is developed for the solution of the data-driven Monge optimal transport barycenter problem, where the pushforward condition is formulated in terms of the statistical independence between two sets of random variables:…
We investigate the approximation of Monge--Kantorovich problems on general compact metric spaces, showing that optimal values, plans and maps can be effectively approximated via a fully discrete method. First we approximate optimal values…
The optimal selection of experimental conditions is essential to maximizing the value of data for inference and prediction, particularly in situations where experiments are time-consuming and expensive to conduct. We propose a general…