Riemannian Laplace Approximation with the Fisher Metric

arXiv:2311.02766v3 Announce Type: replace
Abstract: Laplace's method approximates a target density with a Gaussian distribution at its mode. It is computationally efficient and asymptotically exact for Bayesian inference due to the Bernstein-von Mises theorem, but for complex targets and finite-data posteriors it is often too crude an approximation. A recent generalization of the Laplace Approximation transforms the Gaussian approximation according to a chosen Riemannian geometry providing a richer approximation family, while still retaining computational efficiency. However, as shown here, its …

abstract approximation arxiv bayesian bayesian inference cs.lg data distribution fisher inference laplace approximation stat.me stat.ml targets theorem type