On the convergence of Hamiltonian Monte Carlo

By Alain Oliviero Durmus, Eric Moulines, Eero Saksman. 2017

74 citations recorded by the source corpus.

This paper discusses the irreducibility and geometric ergodicity of the Hamiltonian Monte Carlo (HMC) algorithm. We consider cases where the number of steps of the symplectic integrator is either fixed or random. Under mild conditions on the potential $\F$ associated with target distribution $\pi$, we first show that the Markov kernel associated to the HMC algorithm is irreducible and recurrent. Under more stringent conditions, we then establish that the Markov kernel is Harris recurrent. Finally, we provide verifiable conditions on $\F$ under which the HMC sampler is geometrically ergodic.

Subfields: Mathematical Physics, Numerical Analysis, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/7237a343c2c0bc1707b5925f0b2ebda848905404

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In Mathematical Physics

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Citations in the corpus

• Rapid Convergence of the Unadjusted Langevin Algorithm: Isoperimetry Suffices (2019, background): “When ⌫ is strongly 33rd Conference on Neural Information Processing Systems (NeurIPS 2019), Vancouver, Canada. logconcave, there are many sampling algorithms with provable rapid convergence; these include the ball walk and hit-and-run [37, 43, 44, 42] (which give truly polynomial algorithms), variou”