7 papers
Wasserstein distance estimates for the distributions of numerical approximations to ergodic stochastic differential equations
J. M. Sanz-Serna, Konstantinos C. Zygalakis
We present a framework that allows for the non-asymptotic study of the -Wasserstein distance between the invariant distribution of an ergodic stochastic differential equation an…
Symmetrically processed splitting integrators for enhanced Hamiltonian Monte Carlo sampling
S. Blanes, M. P. Calvo, F. Casas +1
We construct integrators to be used in Hamiltonian (or Hybrid) Monte Carlo sampling. The new integrators are easily implementable and, for a given computational budget, may deliver…
The connections between Lyapunov functions for some optimization algorithms and differential equations
J. M. Sanz-Serna, Konstantinos C. Zygalakis
In this manuscript, we study the properties of a family of second-order differential equations with damping, its discretizations and their connections with accelerated optimization…
Is the NUTS algorithm correct?
J. M. Sanz-Serna
This paper is devoted to investigate whether the popular No U-turn (NUTS) sampling algorithm is correct, i.e.\ whether the target probability distribution is \emph{exactly} conserv…
HMC: avoiding rejections by not using leapfrog and some results on the acceptance rate
M. P. Calvo, D. Sanz-Alonso, J. M. Sanz-Serna
The leapfrog integrator is routinely used within the Hamiltonian Monte Carlo method and its variants. We give strong numerical evidence that alternative, easy to implement algorith…
Contractivity of Runge-Kutta methods for convex gradient systems
J. M. Sanz-Serna, Konstantinos C. Zygalakis
We consider the application of Runge-Kutta (RK) methods to gradient systems , where, as in many optimization problems, is convex and (globall…