Quasi-Newton Hamiltonian Monte Carlo

Tianfan Fu Shanghai Jiao Tong University, Luo Luo Shanghai Jiao Tong University, Zhihua Zhang Shanghai Jiao Tong University
Proceedings of the 32nd Conference on Uncertainty in Artificial Intelligence, PMLR R14:306-315, 2016.

Abstract

The Hamiltonian Monte Carlo (HMC) method has become significantly popular in recent years.It is the state-of-the-art MCMC sampler due to its more efficient exploration to the parameter space than the standard random-walk based proposal.The key idea behind HMC is that it makes use of first-order gradient information about the target distribution. In this paper, we propose a novel dynamics.The new dynamics uses second-order geometric information about the desired distribution.The second-order information is estimated by using a quasi-Newton method (say, the BFGS method), so it does not bring heavy computational burden.Moreover, our theoretical analysis guarantees that this dynamics remains the target distribution invariant.As a result, the proposed quasi-Newton Hamiltonian Monte Carlo (QNHMC) algorithm traverses the parameter space more efficiently than the standard HMC and produces a less correlated series of samples.Finally, empirical evaluation on simulated data verifies the effectiveness and efficiency of our approach.We also conduct applications of QNHMC in Bayesian logistic regression and online Bayesian matrix factorization problems.

Cite this Paper

BibTeX
@InProceedings{pmlr-vR14-university16h, title = {Quasi-{N}ewton {H}amiltonian {M}onte {C}arlo}, author = {University, Tianfan Fu Shanghai Jiao Tong and University, Luo Luo Shanghai Jiao Tong and University, Zhihua Zhang Shanghai Jiao Tong}, booktitle = {Proceedings of the 32nd Conference on Uncertainty in Artificial Intelligence}, pages = {306--315}, year = {2016}, editor = {Ihler, Alexander and Janzing, Dominik}, volume = {R14}, series = {Proceedings of Machine Learning Research}, month = {25--29 Jun}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/r14/main/assets/university16h/university16h.pdf}, url = {https://proceedings.mlr.press/r14/university16h.html}, abstract = {The Hamiltonian Monte Carlo (HMC) method has become significantly popular in recent years.It is the state-of-the-art MCMC sampler due to its more efficient exploration to the parameter space than the standard random-walk based proposal.The key idea behind HMC is that it makes use of first-order gradient information about the target distribution. In this paper, we propose a novel dynamics.The new dynamics uses second-order geometric information about the desired distribution.The second-order information is estimated by using a quasi-Newton method (say, the BFGS method), so it does not bring heavy computational burden.Moreover, our theoretical analysis guarantees that this dynamics remains the target distribution invariant.As a result, the proposed quasi-Newton Hamiltonian Monte Carlo (QNHMC) algorithm traverses the parameter space more efficiently than the standard HMC and produces a less correlated series of samples.Finally, empirical evaluation on simulated data verifies the effectiveness and efficiency of our approach.We also conduct applications of QNHMC in Bayesian logistic regression and online Bayesian matrix factorization problems.}, note = {Reissued by PMLR on 04 October 2026.} }
Endnote
%0 Conference Paper %T Quasi-Newton Hamiltonian Monte Carlo %A Tianfan Fu Shanghai Jiao Tong University %A Luo Luo Shanghai Jiao Tong University %A Zhihua Zhang Shanghai Jiao Tong University %B Proceedings of the 32nd Conference on Uncertainty in Artificial Intelligence %C Proceedings of Machine Learning Research %D 2016 %E Alexander Ihler %E Dominik Janzing %F pmlr-vR14-university16h %I PMLR %P 306--315 %U https://proceedings.mlr.press/r14/university16h.html %V R14 %X The Hamiltonian Monte Carlo (HMC) method has become significantly popular in recent years.It is the state-of-the-art MCMC sampler due to its more efficient exploration to the parameter space than the standard random-walk based proposal.The key idea behind HMC is that it makes use of first-order gradient information about the target distribution. In this paper, we propose a novel dynamics.The new dynamics uses second-order geometric information about the desired distribution.The second-order information is estimated by using a quasi-Newton method (say, the BFGS method), so it does not bring heavy computational burden.Moreover, our theoretical analysis guarantees that this dynamics remains the target distribution invariant.As a result, the proposed quasi-Newton Hamiltonian Monte Carlo (QNHMC) algorithm traverses the parameter space more efficiently than the standard HMC and produces a less correlated series of samples.Finally, empirical evaluation on simulated data verifies the effectiveness and efficiency of our approach.We also conduct applications of QNHMC in Bayesian logistic regression and online Bayesian matrix factorization problems. %Z Reissued by PMLR on 04 October 2026.
APA
University, T.F.S.J.T., University, L.L.S.J.T. & University, Z.Z.S.J.T.. (2016). Quasi-Newton Hamiltonian Monte Carlo. Proceedings of the 32nd Conference on Uncertainty in Artificial Intelligence, in Proceedings of Machine Learning Research R14:306-315 Available from https://proceedings.mlr.press/r14/university16h.html. Reissued by PMLR on 04 October 2026.

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