7 papers
Gradient-free Riemannian Langevin Sampler
Ricardo Baptista, Olivier Zahm
We address the problem of efficiently sampling multimodal probability distributions, where standard Markov Chain Monte Carlo methods often suffer from poor mixing and mode trapping…
A new gradient-free active subspace estimation method with application to rare event probability estimation
Valentin Breaz, Miguel Munoz Zuniga, Olivier Zahm +1
To reduce the cost of estimating the probability of a rare event involving a very large number of random parameters, we propose a new strategy for dimension reduction coupled with…
Sharp detection of low-dimensional structure in probability measures via dimensional logarithmic Sobolev inequalities
Matthew T. C. Li, Tiangang Cui, Fengyi Li +2
Identifying low-dimensional structure in high-dimensional probability measures is an essential pre-processing step for efficient sampling. We introduce a method for identifying and…
Coupled Input-Output Dimension Reduction: Application to Goal-oriented Bayesian Experimental Design and Global Sensitivity Analysis
Qiao Chen, Elise Arnaud, Ricardo Baptista +1
We introduce a new method to jointly reduce the dimension of the input and output space of a function between high-dimensional spaces. Choosing a reduced input subspace influences…
Optimal Riemannian metric for Poincaré inequalities and how to ideally precondition Langevin dynamics
Tiangang Cui, Xin Tong, Olivier Zahm
Poincaré inequality is a fundamental property that rises naturally in different branches of mathematics. The associated Poincaré constant plays a central role in many application…
Sequential transport maps using SoS density estimation and -divergences
Benjamin Zanger, Olivier Zahm, Tiangang Cui +1
Transport-based density estimation methods are receiving growing interest because of their ability to efficiently generate samples from the approximated density. We further inverti…