Hamiltonian Monte Carlo Without Detailed Balance

By Jascha Narain Sohl-Dickstein, Mayur Mudigonda, Michael Robert DeWeese. 2014

66 citations recorded by the source corpus.

We present a method for performing Hamiltonian Monte Carlo that largely eliminates sample rejection for typical hyperparameters. In situations that would normally lead to rejection, instead a longer trajectory is computed until a new state is reached that can be accepted. This is achieved using Markov chain transitions that satisfy the fixed point equation, but do not satisfy detailed balance. The resulting algorithm significantly suppresses the random walk behavior and wasted function evaluations that are typically the consequence of update rejection. We demonstrate a greater than factor of two improvement in mixing time on three test problems. We release the source code as Python and MATLAB packages.

Subfields: Artificial Intelligence, Condensed Matter Physics, Statistics and Probability, Probabilistic & Bayesian Methods

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. Richard E. Turner
2. Fei Sha
3. Sergey Levine
4. Zoubin Ghahramani
5. Yoshua Bengio
6. Wei-Lun Chao
7. Jascha Narain Sohl-Dickstein
8. Yarin Gal

In Condensed Matter Physics

1. Jascha Narain Sohl-Dickstein
2. Daniel Lévy
3. Matthew D. Hoffman
4. Zoubin Ghahramani

In Statistics and Probability

1. Jascha Narain Sohl-Dickstein
2. Zoubin Ghahramani
3. Richard E. Turner
4. Matthew D. Hoffman
5. Daniel Lévy
6. Mayur Mudigonda
7. Michael Robert DeWeese
8. A. Berger

In Probabilistic & Bayesian Methods

1. Jascha Narain Sohl-Dickstein
2. Richard E. Turner
3. Matthew D. Hoffman
4. Daniel Lévy
5. Zoubin Ghahramani
6. David M. Blei
7. Yarin Gal
8. Jun Zhu

Citations in the corpus

• Generalizing Hamiltonian Monte Carlo with Neural Networks (2017, methodology): “We also note that L2HMC could be easily combined with LAHMC, by replacing the leapfrog integrator of LAHMC with the learned one of L2HMC.”
• Exponential Integration for Hamiltonian Monte Carlo (2015, background): “for extensions like (Hoffman & Gelman, 2014) and (Sohl-Dickstein et al., 2014).”
• A Markov Jump Process for More Efficient Hamiltonian Monte Carlo (2015, methodology): “tion techniques [16], Hamiltonian annealed importance sampling [17], split HMC [18], tempered trajectories [9], novel discrete time transition rules [10, 19, 20], stochastic gradient variants on HMC [21], HMC for approximate Bayesian computation [22], and new approximate Hamiltonian integrators [23]”
• Dynamical Sampling with Langevin Normalization Flows (2019, background): “[44] and its energy function is: U(x) = (1)2 x Tx + η ∑i cos( xi η ).”
• Magnetic Hamiltonian Monte Carlo (2016, methodology): “We consider two highly ill-conditioned Gaussians similar to as in (Sohl-Dickstein et al., 2014) to illustrate a heuristic for G matrix selection and demonstrate properties of the magnetic dynamics.”