On log-concave approximations of high-dimensional posterior measures and stability properties in non-linear inverse problems
Abstract
The problem of efficiently generating random samples from high-dimensional and non-log-concave posterior measures arising from nonlinear regression problems is considered. Extending investigations from arXiv:2009.05298, local and global stability properties of the model are identified under which such posterior distributions can be approximated in Wasserstein distance by suitable log-concave measures. This allows the use of fast gradient based sampling algorithms, for which convergence guarantees are established that scale polynomially in all relevant quantities (assuming `warm' initialisation). The scope of the general theory is illustrated in a non-linear inverse problem from integral geometry for which new stability results are derived.
Keywords
Cite
@article{arxiv.2105.07835,
title = {On log-concave approximations of high-dimensional posterior measures and stability properties in non-linear inverse problems},
author = {Jan Bohr and Richard Nickl},
journal= {arXiv preprint arXiv:2105.07835},
year = {2023}
}
Comments
to appear in Ann. Inst. Henri Poincar\'e (Probab. Stat.)