9 citations · 10 across the 7 of their papers we have counts for
10 papers
Theoretical guarantees for stochastic gradient Langevin dynamics
Daniel Paulin, Peter A. Whalley
We prove asymptotic bias bounds for stochastic gradient Langevin dynamics in Wasserstein distance of order two. We assume that the negative log-density is strongly convex with a Li…
Cluster formation for weakly interacting kinetic Langevin dynamics
Benedict Leimkuhler, René Lohmann, Grigorios A. Pavliotis +1
In this paper, we study the formation of clusters for stochastic interacting particle systems (IPS) that interact through short-range attractive potentials in a periodic domain. We…
A Langevin sampling algorithm inspired by the Adam optimizer
Benedict Leimkuhler, René Lohmann, Peter Whalley
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 o…
Sampling from Bayesian Neural Network Posteriors with Symmetric Minibatch Splitting Langevin Dynamics
Daniel Paulin, Peter A. Whalley, Neil K. Chada +1
We propose a scalable kinetic Langevin dynamics algorithm for sampling parameter spaces of big data and AI applications. Our scheme combines a symmetric forward/backward sweep over…
Convergence of kinetic Langevin samplers for non-convex potentials
Katharina Schuh, Peter A. Whalley
We study three kinetic Langevin samplers including the Euler discretization, the BU and the UBU splitting scheme. We provide contraction results in -Wasserstein distance for n…
Correction to "Wasserstein distance estimates for the distributions of numerical approximations to ergodic stochastic differential equations"
Daniel Paulin, Peter A. Whalley
A method for analyzing non-asymptotic guarantees of numerical discretizations of ergodic SDEs in Wasserstein-2 distance is presented by Sanz-Serna and Zygalakis in ``Wasserstein di…
Unbiased Kinetic Langevin Monte Carlo with Inexact Gradients
Neil K. Chada, Benedict Leimkuhler, Daniel Paulin +1
We present an unbiased method for Bayesian posterior means based on kinetic Langevin dynamics that combines advanced splitting methods with enhanced gradient approximations. Our ap…
Contraction Rate Estimates of Stochastic Gradient Kinetic Langevin Integrators
Benedict Leimkuhler, Daniel Paulin, Peter A. Whalley
In previous work, we introduced a method for determining convergence rates for integration methods for the kinetic Langevin equation for -Lipschitz -log-concave densi…
Contraction and Convergence Rates for Discretized Kinetic Langevin Dynamics
Benedict Leimkuhler, Daniel Paulin, Peter A. Whalley
We provide a framework to analyze the convergence of discretized kinetic Langevin dynamics for -Lipschitz, -convex potentials. Our approach gives convergence rates of…
Randomized Time Riemannian Manifold Hamiltonian Monte Carlo
Peter A. Whalley, Daniel Paulin, Benedict Leimkuhler
Hamiltonian Monte Carlo (HMC) algorithms which combine numerical approximation of Hamiltonian dynamics on finite intervals with stochastic refreshment and Metropolis correction are…