Archive for Metropolis adjusted Langevin algorithm
Scalable Monte Carlo for Bayesian Learning [not yet a book review]
Posted in Books, Statistics, University life with tags 1⁰ North, Bayesian learning, book review, Cambridge University Press, continuous time MCMC, convergence diagnostics, cup, Gelman-Rubin statistic, Hamiltonian Monte Carlo, IMS Monographs, kernel Stein discrepancy descent, Markov chain Monte Carlo, MCMC, Metropolis adjusted Langevin algorithm, non-reversible MCMC, North, PDMP, piecewise deterministic, scalable Bayesian learning, scalable MCMC, stochastic differential equation, stochastic gradient MCMC on May 11, 2025 by xi'an
control variates [seminar]
Posted in pictures, Statistics, Travel, University life with tags Athens, CIRM, control variates, convergence of Gibbs samplers, Langevin MCMC algorithm, London, Luminy, MALA, Marseiile, MCMC, Metropolis adjusted Langevin algorithm, Poisson equation, random walk Metropolis algorithm, UCL, University of Warwick on November 5, 2021 by xi'an
Today, Petros Dellaportas (whom I have know since the early days of MCMC, when we met in CIRM) gave a seminar at the Warwick algorithm seminar on control variates for MCMC, reminding me of his 2012 JRSS paper. Based on the Poisson equation and using a second control variate to stabilise the Monte Carlo approximation do the first control variate. The difference with usual control variates is finding a first approximate G(x)-q(y|x)G(Y) to F-πF. And the first Poisson equation is using α(x,y)q(y|x) rather than π. Then the second expands log α(x,y)q(y|x) to achieve a manageable term.
Abstract: We provide a general methodology to construct control variates for any discrete time random walk Metropolis and Metropolis-adjusted Langevin algorithm Markov chains that can achieve, in a post-processing manner and with a negligible additional computational cost, impressive variance reduction when compared to the standard MCMC ergodic averages. Our proposed estimators are based on an approximate solution of the Poisson equation for a multivariate Gaussian target densities of any dimension.
I wonder if there were a neural network version that would first build G from scratch and later optimise it towards solving the Poisson equation. As in this recent arXival I haven’t read (yet).
