Magnetic Hamiltonian Monte Carlo
By Nilesh Tripuraneni, Mark Rowland, Zoubin Ghahramani, Richard E. Turner. 2016
38 citations recorded by the source corpus.
Hamiltonian Monte Carlo (HMC) exploits Hamiltonian dynamics to construct efficient proposals for Markov chain Monte Carlo (MCMC). In this paper, we present a generalization of HMC which exploits \textit{non-canonical} Hamiltonian dynamics. We refer to this algorithm as magnetic HMC, since in 3 dimensions a subset of the dynamics map onto the mechanics of a charged particle coupled to a magnetic field. We establish a theoretical basis for the use of non-canonical Hamiltonian dynamics in MCMC, and construct a symplectic, leapfrog-like integrator allowing for the implementation of magnetic HMC. Finally, we exhibit several examples where these non-canonical dynamics can lead to improved mixing of magnetic HMC relative to ordinary HMC.
Subfields: Probabilistic & Bayesian Methods
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In Probabilistic & Bayesian Methods
- Matthew D. Hoffman
- Jascha Narain Sohl-Dickstein
- Daniel Lévy
- Shiliang Sun
- Yan Liu
- Minghao Gu
- Stefano Ermon
- David M. Blei
Citations in the corpus
- Generalizing Hamiltonian Monte Carlo with Neural Networks (2017, methodology): “…use of alternative HMC accept-reject rules (Sohl-Dickstein et al., 2014; Berger et al., 2015); with the use of non-canonical Hamiltonian dynamics (Tripuraneni et al., 2016); with variants of AIS adapted to HMC proposals (Sohl-Dickstein & Culpepper, 2012); with the extension of HMC to discrete…”
- Dynamical Sampling with Langevin Normalization Flows (2019, methodology): “In other words, the gradients in boundary regions are tremendous and the momentum will increasingly decrease until it changes its direction which makes HMC and MHMC challenging to sample from the target distribution.”