Sampling normalizing constants in high dimensions using inhomogeneous diffusions

2016/12/22 by Christophe Andrieu, Andrieu, Christophe, James Ridgway +3
Mathematics · #FOS: Mathematics #Statistics Theory (math.ST) #math.ST #stat.TH

paper · pdf · doi:10.48550/arxiv.1612.07583

arxiv created 2018/09/06 · arxiv updated 2018/09/07

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 ℝ^d. The main results are nonasymptotic variance and bias bounds, and a central limit theorem in the d→∞ 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.

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