88 citations · 487 across the 78 of their papers we have counts for
15 papers · 1 filter
Second order quantitative bounds for unadjusted generalized Hamiltonian Monte Carlo
Evan Camrud, Alain Durmus, Pierre Monmarché +1
This paper provides a convergence analysis for generalized Hamiltonian Monte Carlo samplers, a family of Markov Chain Monte Carlo methods based on leapfrog integration of Hamiltoni…
Non-asymptotic convergence bounds for Sinkhorn iterates and their gradients: a coupling approach
Giacomo Greco, Maxence Noble, Giovanni Conforti +1
Computational optimal transport (OT) has recently emerged as a powerful framework with applications in various fields. In this paper we focus on a relaxation of the original OT pro…
Quantitative contraction rates for Sinkhorn's algorithm: beyond bounded costs and compact marginals
Giovanni Conforti, Alain Durmus, Giacomo Greco
We show non-asymptotic exponential convergence of Sinkhorn iterates to the Schrödinger potentials, solutions of the quadratic Entropic Optimal Transport problem on .…
Rosenthal-type inequalities for linear statistics of Markov chains
Alain Durmus, Eric Moulines, Alexey Naumov +2
In this paper, we establish novel concentration inequalities for additive functionals of geometrically ergodic Markov chains similar to Rosenthal inequalities for sums of independe…
Sticky nonlinear SDEs and convergence of McKean-Vlasov equations without confinement
Alain Durmus, Andreas Eberle, Arnaud Guillin +1
We develop a new approach to study the long time behaviour of solutions to nonlinear stochastic differential equations in the sense of McKean, as well as propagation of chaos for t…
Probability and moment inequalities for additive functionals of geometrically ergodic Markov chains
Alain Durmus, Eric Moulines, Alexey Naumov +1
In this paper, we establish moment and Bernstein-type inequalities for additive functionals of geometrically ergodic Markov chains. These inequalities extend the corresponding ineq…
Asymptotic bias of inexact Markov Chain Monte Carlo methods in high dimension
Alain Oliviero Durmus, Andreas Eberle
Inexact Markov Chain Monte Carlo methods rely on Markov chains that do not exactly preserve the target distribution. Examples include the unadjusted Langevin algorithm (ULA) and un…
Uniform minorization condition and convergence bounds for discretizations of kinetic Langevin dynamics
Alain Durmus, Aurélien Enfroy, Éric Moulines +1
We study the convergence in total variation and -norm of discretization schemes of the underdamped Langevin dynamics. Such algorithms are very popular and commonly used in molec…
Discrete sticky couplings of functional autoregressive processes
Alain Durmus, Andreas Eberle, Aurélien Enfroy +2
In this paper, we provide bounds in Wasserstein and total variation distances between the distributions of the successive iterates of two functional autoregressive processes with i…
Convergence of diffusions and their discretizations: from continuous to discrete processes and back
Valentin De Bortoli, Alain Durmus
In this paper, we establish new quantitative convergence bounds for a class of functional autoregressive models in weighted total variation metrics. To derive our results, we show…
Piecewise Deterministic Markov Processes and their invariant measures
Alain Durmus, Arnaud Guillin, Pierre Monmarché
Piecewise Deterministic Markov Processes (PDMPs) are studied in a general framework. First, different constructions are proven to be equivalent. Second, we introduce a coupling bet…
Geometric ergodicity of the bouncy particle sampler
Alain Durmus, Arnaud Guillin, Pierre Monmarché
The Bouncy Particle Sampler (BPS) is a Monte Carlo Markov Chain algorithm to sample from a target density known up to a multiplicative constant. This method is based on a kinetic p…
An Elementary Approach To Uniform In Time Propagation Of Chaos
Alain Durmus, Andreas Eberle, Arnaud Guillin +1
Based on a coupling approach, we prove uniform in time propagation of chaos for weakly interacting mean-field particle systems with possibly non-convex confinement and interaction…
Optimal scaling of the Random Walk Metropolis algorithm under Lp mean differentiability
Alain Durmus, Sylvain Le Corff, Eric Moulines +1
This paper considers the optimal scaling problem for high-dimensional random walk Metropolis algorithms for densities which are differentiable in Lp mean but which may be irregular…
Subgeometric rates of convergence in Wasserstein distance for Markov chains
Alain Durmus, Gersende Fort, Eric Moulines
In this paper, we provide sufficient conditions for the existence of the invariant distribution and for subgeometric rates of convergence in Wasserstein distance for general state-…