Randomized Hamiltonian Monte Carlo as scaling limit of the bouncy particle sampler and dimension-free convergence rates
The Bouncy Particle Sampler is a Markov chain Monte Carlo method based on a nonreversible piecewise deterministic Markov process. In this scheme, a particle explores the state space of interest by evolving according to a linear dynamics which is altered by bouncing on the hyperplane tangent to the g...
| Hoofdauteurs: | , , , |
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| Formaat: | Journal article |
| Taal: | English |
| Gepubliceerd in: |
Institute of Mathematical Statistics
2021
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| _version_ | 1826303530938400768 |
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| author | Deligiannidis, G Paulin, D Bouchard-Côté, A Doucet, A |
| author_facet | Deligiannidis, G Paulin, D Bouchard-Côté, A Doucet, A |
| author_sort | Deligiannidis, G |
| collection | OXFORD |
| description | The Bouncy Particle Sampler is a Markov chain Monte Carlo method based on a nonreversible piecewise deterministic Markov process. In this scheme, a particle explores the state space of interest by evolving according to a linear dynamics which is altered by bouncing on the hyperplane tangent to the gradient of the negative log-target density at the arrival times of an inhomogeneous Poisson Process (PP) and by randomly perturbing its velocity at the arrival times of an homogeneous PP. Under regularity conditions, we show here that the process corresponding to the first component of the particle and its corresponding velocity converges weakly towards a Randomized Hamiltonian Monte Carlo (RHMC) process as the dimension of the ambient space goes to infinity. RHMC is another piecewise deterministic non-reversible Markov process where a Hamiltonian dynamics is altered at the arrival times of a homogeneous PP by randomly perturbing the momentum component. We then establish dimension-free convergence rates for RHMC for strongly log-concave targets with bounded Hessians using coupling ideas and hypocoercivity techniques. |
| first_indexed | 2024-03-07T06:04:06Z |
| format | Journal article |
| id | oxford-uuid:ed3ee466-c948-4fb8-8ba3-ed98db948a9f |
| institution | University of Oxford |
| language | English |
| last_indexed | 2024-03-07T06:04:06Z |
| publishDate | 2021 |
| publisher | Institute of Mathematical Statistics |
| record_format | dspace |
| spelling | oxford-uuid:ed3ee466-c948-4fb8-8ba3-ed98db948a9f2022-03-27T11:23:31ZRandomized Hamiltonian Monte Carlo as scaling limit of the bouncy particle sampler and dimension-free convergence ratesJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:ed3ee466-c948-4fb8-8ba3-ed98db948a9fEnglishSymplectic Elements at OxfordInstitute of Mathematical Statistics2021Deligiannidis, GPaulin, DBouchard-Côté, ADoucet, AThe Bouncy Particle Sampler is a Markov chain Monte Carlo method based on a nonreversible piecewise deterministic Markov process. In this scheme, a particle explores the state space of interest by evolving according to a linear dynamics which is altered by bouncing on the hyperplane tangent to the gradient of the negative log-target density at the arrival times of an inhomogeneous Poisson Process (PP) and by randomly perturbing its velocity at the arrival times of an homogeneous PP. Under regularity conditions, we show here that the process corresponding to the first component of the particle and its corresponding velocity converges weakly towards a Randomized Hamiltonian Monte Carlo (RHMC) process as the dimension of the ambient space goes to infinity. RHMC is another piecewise deterministic non-reversible Markov process where a Hamiltonian dynamics is altered at the arrival times of a homogeneous PP by randomly perturbing the momentum component. We then establish dimension-free convergence rates for RHMC for strongly log-concave targets with bounded Hessians using coupling ideas and hypocoercivity techniques. |
| spellingShingle | Deligiannidis, G Paulin, D Bouchard-Côté, A Doucet, A Randomized Hamiltonian Monte Carlo as scaling limit of the bouncy particle sampler and dimension-free convergence rates |
| title | Randomized Hamiltonian Monte Carlo as scaling limit of the bouncy particle sampler and dimension-free convergence rates |
| title_full | Randomized Hamiltonian Monte Carlo as scaling limit of the bouncy particle sampler and dimension-free convergence rates |
| title_fullStr | Randomized Hamiltonian Monte Carlo as scaling limit of the bouncy particle sampler and dimension-free convergence rates |
| title_full_unstemmed | Randomized Hamiltonian Monte Carlo as scaling limit of the bouncy particle sampler and dimension-free convergence rates |
| title_short | Randomized Hamiltonian Monte Carlo as scaling limit of the bouncy particle sampler and dimension-free convergence rates |
| title_sort | randomized hamiltonian monte carlo as scaling limit of the bouncy particle sampler and dimension free convergence rates |
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