5 papers
Continuous transformations of probability measures and their transport representations
Hugo Lavenant, Giuseppe Savaré
Given a function transforming a probability measure into another one , we study the existence and regularity of a transport representation of it. That is, we ask wh…
Measures of Dependence based on Wasserstein distances
Marta Catalano, Hugo Lavenant
Measuring dependence between random variables is a fundamental problem in Statistics, with applications across diverse fields. While classical measures such as Pearson's correlatio…
Measuring Partial Exchangeability with Reproducing Kernel Hilbert Spaces
Marta Catalano, Hugo Lavenant, Francesco Mascari
In Bayesian multilevel models, the data are structured in interconnected groups, and their posteriors borrow information from one another due to prior dependence between latent par…
Quantitative convergence of a discretization of dynamic optimal transport using the dual formulation
Sadashige Ishida, Hugo Lavenant
We present a discretization of the dynamic optimal transport problem for which we can obtain the convergence rate for the value of the transport cost to its continuous value when t…
Lifting functionals defined on maps to measure-valued maps via optimal transport
Hugo Lavenant
How can one lift a functional defined on maps from a space X to a space Y into a functional defined on maps from X into P(Y) the space of probability distributions over Y? Looking…