Optimal transport (OT) theory can be informally described using the words of the French
mathematician Gaspard Monge (1746–1818): A worker with a shovel in hand has to move a …

Markov chain Monte Carlo methods are often deemed too computationally intensive to be of
any practical use for big data applications, and in particular for inference on datasets …

This paper deals with the problem of quantifying the impact of model misspecification when
computing general expected values of interest. The methodology that we propose is …

We show that several machine learning estimators, including square-root least absolute
shrinkage and selection and regularized logistic regression, can be represented as …

Fusing probabilistic information is a fundamental task in signal and data processing with
relevance to many fields of technology and science. In this work, we investigate the fusion of …

The use of Bayesian methods in large-scale data settings is attractive because of the rich
hierarchical models, uncertainty quantification, and prior specification they provide …

Wasserstein distance plays increasingly important roles in machine learning, stochastic
programming and image processing. Major efforts have been under way to address its high …

Optimal transport maps between two probability distributions $\mu $ and $\nu $ on $\R^ d $
have found extensive applications in both machine learning and statistics. In practice, these …

A growing number of generative statistical models do not permit the numerical evaluation of
their likelihood functions. Approximate Bayesian computation has become a popular …

We provide theoretical analyses for two algorithms that solve the regularized optimal
transport (OT) problem between two discrete probability measures with at most $ n $ atoms …