Can I read Hypocoercivity properties of adaptive Langevin dynamics on EtoBox?

Hypocoercivity properties of adaptive Langevin dynamics by Leimkuhler, Benedict; Sachs, Matthias; Stoltz, Gabriel is a scholarly article available to read on EtoBox.

What is Hypocoercivity properties of adaptive Langevin dynamics about?

Adaptive Langevin dynamics is a method for sampling the Boltzmann-Gibbs distribution at prescribed temperature in cases where the potential gradient is subject to stochastic perturbation of unknown magnitude. The method replaces the friction in underdamped Langevin dynamics with a dynamical variable, updated according to a negative feedback loop control law as in the Nos\'e-Hoover thermostat. Using a hypocoercivity analysis we show that the law of Adaptive Langevin dynamics converges exponentially rapidly to the stationary distribution, with a rate that can be quantified in terms of the key parameters of the dynamics. This allows us in particular to obtain a central limit theorem with respect to the time averages computed along a stochastic path. Our theoretical findings are illustrated by numerical simulations involving classification of the MNIST data set of handwritten digits using Bayesian logistic regression.

Author

Leimkuhler, Benedict; Sachs, Matthias; Stoltz, Gabriel

Published

2019

Language

EN