English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

Hamiltonian Monte Carlo (HMC) is a state-of-the-art Markov chain Monte Carlosampling algorithm for drawing samples from smooth probability densities overcontinuous spaces. We study the variant most widely used in practice,Metropolized HMC with the St\"{o}rmer-Verlet or leapfrog integrator, and maketwo primary contributions. First, we provide a non-asymptotic upper bound onthe mixing time of the Metropolized HMC with explicit choices of step-size andnumber of leapfrog steps. This bound gives a precise quantification of thefaster convergence of Metropolized HMC relative to simpler MCMC algorithms suchas the Metropolized random walk, or Metropolized Langevin algorithm. Second, weprovide a general framework for sharpening mixing time bounds of Markov chainsinitialized at a substantial distance from the target distribution overcontinuous spaces. We apply this sharpening device to the Metropolized randomwalk and Langevin algorithms, thereby obtaining improved mixing time boundsfrom a non-warm initial distribution.

Fast mixing of Metropolized Hamiltonian Monte Carlo: Benefits of multi-step gradients