Related papers: Adaptive stepsize algorithms for Langevin dynamics
We consider numerical methods for thermodynamic sampling, i.e. computing sequences of points distributed according to the Gibbs-Boltzmann distribution, using Langevin dynamics and overdamped Langevin dynamics (Brownian dynamics). A wide…
We present a framework for adaptive-stepsize MCMC sampling based on time-rescaled Langevin dynamics, in which the stepsize variation is dynamically driven by an additional degree of freedom. Our approach augments the phase space by an…
Langevin algorithms are popular Markov chain Monte Carlo methods that are often used to solve high-dimensional large-scale sampling problems in machine learning. The most classical Langevin Monte Carlo algorithm is based on the overdamped…
How can we learn the laws underlying the dynamics of stochastic systems when their trajectories are sampled sparsely in time? Existing methods either require temporally resolved high-frequency observations, or rely on geometric arguments…
In this paper we introduce and analyse Langevin samplers that consist of perturbations of the standard underdamped Langevin dynamics. The perturbed dynamics is such that its invariant measure is the same as that of the unperturbed dynamics.…
The Langevin dynamics is a diffusion process extensively used, in particular in molecular dynamics simulations, to sample Gibbs measures. Some alternatives based on (piecewise deterministic) kinetic velocity jump processes have gained…
Constrained sampling is an important and challenging task in computational statistics, concerned with generating samples from a distribution under certain constraints. There are numerous types of algorithm aimed at this task, ranging from…
The measured time series from complex systems are renowned for their intricate stochastic behavior, characterized by random fluctuations stemming from external influences and nonlinear interactions. These fluctuations take diverse forms,…
We study numerical methods for sampling probability measures in high dimension where the underlying model is only approximately identified with a gradient system. Extended stochastic dynamical methods are discussed which have application to…
We study the convergence to equilibrium of an underdamped Langevin equation that is controlled by a linear feedback force. Specifically, we are interested in sampling the possibly multimodal invariant probability distribution of a Langevin…
When simulating molecular systems using deterministic equations of motion (e.g., Newtonian dynamics), such equations are generally numerically integrated according to a well-developed set of algorithms that share commonly agreed-upon…
We consider the problem of scalable sampling algorithms to fit Bayesian generalized linear mixed models on large datasets. Stochastic gradient Langevin dynamics, coupled with smooth re-parameterizations of variance parameters, produces…
In this paper we propose a new approach for sampling from probability measures in, possibly, high dimensional spaces. By perturbing the standard overdamped Langevin dynamics by a suitable Stratonovich perturbation that preserves the…
This article considers the application of Langevin dynamics to sampling and investigates how to choose the damping parameter in Langevin dynamics for the purpose of maximizing thoroughness of sampling. Also, it considers the computation of…
We propose a novel approach for performing dynamical system identification, based upon the comparison of simulated and observed physical invariant measures. While standard methods adopt a Lagrangian perspective by directly treating…
We study the design and implementation of numerical methods to solve the generalized Langevin equation (GLE) focusing on canonical sampling properties of numerical integrators. For this purpose, we cast the GLE in an extended phase space…
A systematic procedure for optimising the friction coefficient in underdamped Langevin dynamics as a sampling tool is given by taking the gradient of the associated asymptotic variance with respect to friction. We give an expression for…
A fully Bayesian treatment of complicated predictive models (such as deep neural networks) would enable rigorous uncertainty quantification and the automation of higher-level tasks including model selection. However, the intractability of…
We develop a novel class of MCMC algorithms based on a stochastized Nesterov scheme. With an appropriate addition of noise, the result is a time-inhomogeneous underdamped Langevin equation, which we prove emits a specified target…
The problem of designing adaptive stepsize sequences for the gradient descent method applied to convex and locally smooth functions is studied. We take an adaptive control perspective and design update rules for the stepsize that make use…