Hybrid Monte Carlo on Hilbert spaces

By Alexandros Beskos, Francis J. Pinski, Jesús María Sanz-Serna, Andrew M. Stuart. 2011

155 citations recorded by the source corpus.

Subfields: Artificial Intelligence, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/4a7efd34691690c929d44ffa1458cea2bff865e2

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Artificial Intelligence

1. Mark A. Girolami
2. Jascha Narain Sohl-Dickstein
3. Andrew M. Stuart
4. Masoumeh Dashti
5. Michael Betancourt
6. Gareth O. Roberts
7. Mayur Mudigonda
8. Michael Robert DeWeese

In Statistics and Probability

1. Andrew M. Stuart
2. Mark A. Girolami
3. Michael Betancourt
4. Jascha Narain Sohl-Dickstein
5. Masoumeh Dashti
6. Sandra Jeanne Vollmer
7. Simon Byrne
8. Marcelo Pereyra

Citations in the corpus

• Spectral gaps for a Metropolis–Hastings algorithm in infinite dimensions (2011, methodology): “There are also variants of the Metropolis-adjusted Langevin algorithm (MALA) [5], as well as Hybrid Monte-Carlo methods [3] adapted to the sampling of measures defined via density w.”
• The Geometric Foundations of Hamiltonian Monte Carlo (2014, background): “Algorithms on infinite-dimensional spaces motivated by Hamiltonian Monte Carlo, however, have shown promise (Beskos et al., 2011) and suggest that infinite-dimensional manifolds admit symplectic structures, or the appropriate generalizations thereof.”
• The Bayesian Approach to Inverse Problems (2013, background): “a is generalized to certain conditioned hypoelliptic diffusions in [HSV11b]. It is also possible to study deterministic Hamiltonian dynamics which preserves the same measure. This idea is described in [BPSSS11] in the same set-up as employed here; that paper also contains references to the wider lite”
• A Markov Jump Process for More Efficient Hamiltonian Monte Carlo (2015, methodology): “These include the use of shadow Hamiltonians that are more closely conserved by the approximate Hamiltonian integrator [11], Riemann manifold HMC [12] and other investigation of its geometry [13], quasi-Newton HMC [14], Hilbert space HMC [15], parameter adapta-”
• MCMC Methods for Functions: ModifyingOld Algorithms to Make Them Faster (2012, methodology): “It is hence of interest to generalize these methods to the function sampling setting dictated by (1.1) and this is undertaken in [6].”
• Hamiltonian Monte Carlo Without Detailed Balance (2014, methodology): “These include Riemann manifold HMC (Girolami & Calderhead, 2011), quasi-Newton HMC (Zhang & Sutton, 2011), Hilbert space HMC (Beskos et al., 2011), shadow Hamiltonian methods (Izaguirre & Hampton, 2004), parameter adaptation techniques (Wang et al., 2013), Hamiltonian annealed importance sampling…”