Related papers: Beyond entropic regularization: Debiased Gaussian …
We study the entropic regularizations of optimal transport problems under suitable summability assumptions on the point-wise transport cost. These summability assumptions already appear in the literature. However, we show that the weakest…
We propose to tackle the problem of understanding the effect of regularization in Sinkhorn algotihms. In the case of Gaussian distributions we provide a closed form for the regularized optimal transport which enables to provide a better…
We develop a novel and general framework for reduced-bias $M$-estimation from asymptotically unbiased estimating functions. The framework relies on an empirical approximation of the bias by a function of derivatives of estimating function…
Maximum consensus estimation plays a critically important role in robust fitting problems in computer vision. Currently, the most prevalent algorithms for consensus maximization draw from the class of randomized hypothesize-and-verify…
We propose a stochastic representation for a simple class of transport PDEs based on Ito representations. We detail an algorithm using an estimator stemming for the representation that, unlike regularization by noise estimators, is…
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…
This paper studies the equitable and optimal transport (EOT) problem, which has many applications such as fair division problems and optimal transport with multiple agents etc. In the discrete distributions case, the EOT problem can be…
The Optimal Transport (OT) problem with squared Euclidean cost consists in finding a coupling between two input measures that maximizes correlation. Consequently, the optimal coupling is often singular with respect to the Lebesgue measure.…
We investigate an empirical Bayesian nonparametric approach to a family of linear inverse problems with Gaussian prior and Gaussian noise. We consider a class of Gaussian prior probability measures with covariance operator indexed by a…
We consider the problem of uncertainty estimation in the context of (non-Bayesian) deep neural classification. In this context, all known methods are based on extracting uncertainty signals from a trained network optimized to solve the…
This article details a general numerical framework to approximate so-lutions to linear programs related to optimal transport. The general idea is to introduce an entropic regularization of the initial linear program. This regularized…
Within the statistical and machine learning literature, regularization techniques are often used to construct sparse (predictive) models. Most regularization strategies only work for data where all predictors are treated identically, such…
Motivated by the poor performance of cross-validation in settings where data are scarce, we propose a novel estimator of the out-of-sample performance of a policy in data-driven optimization.Our approach exploits the optimization problem's…
Compute and memory constraints have historically prevented traffic simulation software users from fully utilizing the predictive models underlying them. When calibrating car-following models, particularly, accommodations have included 1)…
Adding entropic regularization to Optimal Transport (OT) problems has become a standard approach for designing efficient and scalable solvers. However, regularization introduces a bias from the true solution. To mitigate this bias while…
In this work, we introduce a novel strategy for tackling constrained optimization problems through a modified penalty method. Conventional penalty methods convert constrained problems into unconstrained ones by incorporating constraints…
Regularization methods are often employed in deep learning neural networks (DNNs) to prevent overfitting. For penalty based DNN regularization methods, convex penalties are typically considered because of their optimization guarantees.…
Bayesian Optimization using Gaussian Processes is a popular approach to deal with the optimization of expensive black-box functions. However, because of the a priori on the stationarity of the covariance matrix of classic Gaussian…
We tackle the problem of building adaptive estimation procedures for ill-posed inverse problems. For general regularization methods depending on tuning parameters, we construct a penalized method that selects the optimal smoothing sequence…
Deep-learning models for traffic data prediction can have superior performance in modeling complex functions using a multi-layer architecture. However, a major drawback of these approaches is that most of these approaches do not offer…