相关论文: Vector quantile regression and optimal transport, …

Quantile regression (QR) is a statistical tool for distribution-free estimation of conditional quantiles of a target variable given explanatory features. QR is limited by the assumption that the target distribution is univariate and defined…

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 establish a connection between Optimal Transport Theory and classical Convection Theory for geophysical flows. Our starting point is the model designed few years ago by Angenent, Haker and Tannenbaum to solve some Optimal Transport…

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.…

We study distributed optimization problems over a network when the communication between the nodes is constrained, and so information that is exchanged between the nodes must be quantized. This imperfect communication poses a fundamental…

Many research has been conducted about quadratic programming and inverse optimization. In this paper we present the combination aspect of these subjects, applying on transportation problem. First, we obtain the inverse form of quadratic…

We consider a multi-armed bandit problem with covariates. Given a realization of the covariate vector, instead of targeting the treatment with highest conditional expectation, the decision maker targets the treatment which maximizes a…

We introduce a new class of convex-regularized Optimal Transport losses, which generalizes the classical Entropy-regularization of Optimal Transport and Sinkhorn divergences, and propose a generalized Sinkhorn algorithm. Our framework…

We extend the analysis of investment strategies derived from penalized quantile regression models, introducing alternative approaches to improve state\textendash of\textendash art asset allocation rules. First, we use a post\textendash…

Optimal transportation provides a means of lifting distances between points on a geometric domain to distances between signals over the domain, expressed as probability distributions. On a graph, transportation problems can be used to…

Optimal transport on a graph focuses on finding the most efficient way to transfer resources from one distribution to another while considering the graph's structure. This paper introduces a new distributed algorithm that solves the optimal…

Following [21, 23], the present work investigates a new relative entropy-regularized algorithm for solving the optimal transport on a graph problem within the randomized shortest paths formalism. More precisely, a unit flow is injected into…

In vector quantization the number of vectors used to construct the codebook is always an undefined problem, there is always a compromise between the number of vectors and the quantity of information lost during the compression. In this text…

We investigate the problem of sampling from posterior distributions with intractable normalizing constants in Bayesian inference. Our solution is a new generative modeling approach based on optimal transport (OT) that learns a deterministic…

Presently, the main methods for describing a non-equilibrium charge-transporting steady state are based on time-evolving it from the initial zero-current situation. An alternative class of theories would give the statistical non-equilibrium…

The traveling salesman problem is a fundamental combinatorial optimization problem with strong exact algorithms. However, as problems scale up, these exact algorithms fail to provide a solution in a reasonable time. To resolve this, current…

Poisson distributed measurements in inverse problems often stem from Poisson point processes that are observed through discretized or finite-resolution detectors, one of the most prominent examples being positron emission tomography (PET).…

We consider two different variational models of transport networks, the so-called branched transport problem and the urban planning problem. Based on a novel relation to Mumford-Shah image inpainting and techniques developed in that field,…

We propose a new algorithm for variance reduction when estimating $f(X_T)$ where $X$ is the solution to some stochastic differential equation and $f$ is a test function. The new estimator is $(f(X^1_T) + f(X^2_T))/2$, where $X^1$ and $X^2$…

We consider inverse problems in Hilbert spaces under correlated Gaussian noise and use a Bayesian approach to find their regularised solution. We focus on mildly ill-posed inverse problems with the noise being generalised derivative of…