Magnetic Hamiltonian Monte Carlo
This work addresses the challenge of slow mixing in MCMC methods for Bayesian inference, offering a potential improvement over standard HMC, though it appears incremental as a generalization of existing techniques.
The paper tackles the problem of improving Markov chain Monte Carlo (MCMC) efficiency by generalizing Hamiltonian Monte Carlo (HMC) to use non-canonical Hamiltonian dynamics, referred to as magnetic HMC, and demonstrates that this approach can lead to improved mixing compared to ordinary HMC in several examples.
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.