9 citations · 18 across the 12 of their papers we have counts for
13 papers
Bernstein--von Mises theorems for Bayesian probabilistic numerics
Sascha Gaudlitz, Sven Wang
We study probabilistic numerical methods for solving nonlinear PDEs from a Bayesian nonparametric perspective. Given noisy evaluations at random collocation points, we place a trun…
Global polynomial-time estimation in statistical nonlinear inverse problems via generalized stability
Sven Wang
Non-linear statistical inverse problems pose major challenges both for statistical analysis and computation. Likelihood-based estimators typically lead to non-convex and possibly m…
Statistical Learning Theory for Neural Operators
Niklas Reinhardt, Sven Wang, Jakob Zech
We present statistical convergence results for the learning of (possibly) non-linear mappings in infinite-dimensional spaces. Specifically, given a map $G_0:\mathcal X\to\mathcal Y…
Statistical algorithms for low-frequency diffusion data: A PDE approach
Matteo Giordano, Sven Wang
We consider the problem of making nonparametric inference in a class of multi-dimensional diffusions in divergence form, from low-frequency data. Statistical analysis in this setti…
Wasserstein-based Minimax Estimation of Dependence in Multivariate Regularly Varying Extremes
Xuhui Zhang, Jose Blanchet, Youssef Marzouk +2
We present the first minimax risk bounds for estimators of the spectral measure in multivariate linear factor models, where observations are linear combinations of regularly varyin…
Distribution learning via neural differential equations: a nonparametric statistical perspective
Youssef Marzouk, Zhi Ren, Sven Wang +1
Ordinary differential equations (ODEs), via their induced flow maps, provide a powerful framework to parameterize invertible transformations for the purpose of representing complex…
Infinite-Dimensional Diffusion Models
Jakiw Pidstrigach, Youssef Marzouk, Sebastian Reich +1
Diffusion models have had a profound impact on many application areas, including those where data are intrinsically infinite-dimensional, such as images or time series. The standar…
On free energy barriers in Gaussian priors and failure of cold start MCMC for high-dimensional unimodal distributions
Afonso S. Bandeira, Antoine Maillard, Richard Nickl +1
We exhibit examples of high-dimensional unimodal posterior distributions arising in non-linear regression models with Gaussian process priors for which MCMC methods can take an exp…
On minimax density estimation via measure transport
Sven Wang, Youssef Marzouk
We study the convergence properties, in Hellinger and related distances, of nonparametric density estimators based on measure transport. These estimators represent the measure of i…
Distributionally Robust Gaussian Process Regression and Bayesian Inverse Problems
Xuhui Zhang, Jose Blanchet, Youssef Marzouk +2
We study a distributionally robust optimization formulation (i.e., a min-max game) for two representative problems in Bayesian nonparametric estimation: Gaussian process regression…
Laplace priors and spatial inhomogeneity in Bayesian inverse problems
Sergios Agapiou, Sven Wang
Spatially inhomogeneous functions, which may be smooth in some regions and rough in other regions, are modelled naturally in a Bayesian manner using so-called Besov priors which ar…
On polynomial-time computation of high-dimensional posterior measures by Langevin-type algorithms
Richard Nickl, Sven Wang
The problem of generating random samples of high-dimensional posterior distributions is considered. The main results consist of non-asymptotic computational guarantees for Langevin…
The nonparametric LAN expansion for discretely observed diffusions
Sven Wang
Consider a scalar reflected diffusion , where the unknown drift function is modelled nonparametrically. We show that in the low frequency sampling case, when the…