41 citations · 198 across the 24 of their papers we have counts for
28 papers
Certified Bayesian optimal experimental design: from Expected Information Gain to Signal-to-Noise Ratio
Mohamed Doumbouya, Arthur Vidard, Olivier Zahm
Optimal experimental design is often formulated as the maximization of the Expected Information Gain (EIG), which measures the expected reduction in uncertainty about a parameter o…
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…
Continuous Gaussian mixture solution for linear Bayesian inversion with application to Laplace priors
Rafael Flock, Yiqiu Dong, Felipe Uribe +1
We focus on Bayesian inverse problems with Gaussian likelihood, linear forward model, and priors that can be formulated as a Gaussian mixture. Such a mixture is expressed as an int…
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…
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…
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 applications…
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…
Principal Feature Detection via -Sobolev Inequalities
Matthew T. C. Li, Youssef Marzouk, Olivier Zahm
We investigate the approximation of high-dimensional target measures as low-dimensional updates of a dominating reference measure. This approximation class replaces the associated…
Self-reinforced polynomial approximation methods for concentrated probability densities
Tiangang Cui, Sergey Dolgov, Olivier Zahm
Transport map methods offer a powerful statistical learning tool that can couple a target high-dimensional random variable with some reference random variable using invertible tran…
Gradient-based data and parameter dimension reduction for Bayesian models: an information theoretic perspective
Ricardo Baptista, Youssef Marzouk, Olivier Zahm
We consider the problem of reducing the dimensions of parameters and data in non-Gaussian Bayesian inference problems. Our goal is to identify an "informed" subspace of the paramet…
Prior normalization for certified likelihood-informed subspace detection of Bayesian inverse problems
Tiangang Cui, Xin Tong, Olivier Zahm
Markov chain Monte Carlo (MCMC) methods form one of the algorithmic foundations of Bayesian inverse problems. The recent development of likelihood-informed subspace (LIS) methods o…
Scalable conditional deep inverse Rosenblatt transports using tensor-trains and gradient-based dimension reduction
Tiangang Cui, Sergey Dolgov, Olivier Zahm
We present a novel offline-online method to mitigate the computational burden of the characterization of posterior random variables in statistical learning. In the offline phase, t…
Data-Free Likelihood-Informed Dimension Reduction of Bayesian Inverse Problems
Tiangang Cui, Olivier Zahm
Identifying a low-dimensional informed parameter subspace offers a viable path to alleviating the dimensionality challenge in the sampled-based solution to large-scale Bayesian inv…
Nonlinear dimension reduction for surrogate modeling using gradient information
Daniele Bigoni, Youssef Marzouk, Clémentine Prieur +1
We introduce a method for the nonlinear dimension reduction of a high-dimensional function , . Our objective is to identify a nonlinear…
Learning non-Gaussian graphical models via Hessian scores and triangular transport
Ricardo Baptista, Youssef Marzouk, Rebecca E. Morrison +1
Undirected probabilistic graphical models represent the conditional dependencies, or Markov properties, of a collection of random variables. Knowing the sparsity of such a graphica…
Minimizing rational functions: a hierarchy of approximations via pushforward measures
Jean Bernard Lasserre, Victor Magron, Swann Marx +1
This paper is concerned with minimizing a sum of rational functions over a compact set of high-dimension. Our approach relies on the second Lasserre's hierarchy (also known as the…
On the representation and learning of monotone triangular transport maps
Ricardo Baptista, Youssef Marzouk, Olivier Zahm
Transportation of measure provides a versatile approach for modeling complex probability distributions, with applications in density estimation, Bayesian inference, generative mode…
Randomized residual-based error estimators for the Proper Generalized Decomposition approximation of parametrized problems
Kathrin Smetana, Olivier Zahm
This paper introduces a novel error estimator for the Proper Generalized Decomposition (PGD) approximation of parametrized equations. The estimator is intrinsically random: It buil…
Greedy inference with structure-exploiting lazy maps
Michael C. Brennan, Daniele Bigoni, Olivier Zahm +2
We propose a framework for solving high-dimensional Bayesian inference problems using \emph{structure-exploiting} low-dimensional transport maps or flows. These maps are confined t…
Multifidelity Dimension Reduction via Active Subspaces
Rémi Lam, Olivier Zahm, Youssef Marzouk +1
We propose a multifidelity dimension reduction method to identify a low-dimensional structure present in many engineering models. The structure of interest arises when functions va…
Randomized residual-based error estimators for parametrized equations
Kathrin Smetana, Olivier Zahm, Anthony T Patera
We propose a randomized a posteriori error estimator for reduced order approximations of parametrized (partial) differential equations. The error estimator has several important pr…
Certified dimension reduction in nonlinear Bayesian inverse problems
Olivier Zahm, Tiangang Cui, Kody Law +2
We propose a dimension reduction technique for Bayesian inverse problems with nonlinear forward operators, non-Gaussian priors, and non-Gaussian observation noise. The likelihood f…
Gradient-based dimension reduction of multivariate vector-valued functions
Olivier Zahm, Paul Constantine, Clémentine Prieur +1
Multivariate functions encountered in high-dimensional uncertainty quantification problems often vary most strongly along a few dominant directions in the input parameter space. We…