Sampling normalizing constants in high dimensions using inhomogeneous diffusions

Abstract

Motivated by the task of computing normalizing constants and importance sampling in high dimensions, we study the dimension dependence of fluctuations for additive functionals of time-inhomogeneous Langevin-type diffusions on ${\mathbb{R}}^d$. The main results are nonasymptotic variance and bias bounds, and a central limit theorem in the $d\to \infty$ regime. We demonstrate that a temporal discretization inherits the fluctuation properties of the underlying diffusion, which are controlled at a computational cost growing at most polynomially with $d$. The key steps include establishing Poincaré inequalities for time-marginal distributions of the diffusion and nonasymptotic bounds on deviation from Gaussianity in a martingale central limit theorem.

References in corpus (1)

• Non-asymptotic convergence analysis for the Unadjusted Langevin Algorithm

Cited by in corpus (2)

• Unbiased estimation of log normalizing constants with applications to Bayesian cross-validation
• Estimating Normalizing Constants for Log-Concave Distributions: Algorithms and Lower Bounds