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Publication - Professor Christophe Andrieu

    Sampling normalizing constants in high dimensions using inhomogeneous diffusions

    Citation

    Andrieu, C, Ridgway, J & Whiteley, N, 2016, ‘Sampling normalizing constants in high dimensions using inhomogeneous diffusions’. arXiv.

    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
    Rd. 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 technical steps include establishing Poincar\'e
    inequalities for time-marginal distributions of the diffusion and nonasymptotic
    bounds on deviation from Gaussianity in a martingale central limit theorem.

    Full details in the University publications repository