Probabilistic Path Hamiltonian Monte Carlo

Vu Dinh, Arman Bilge, Cheng Zhang, Frederick A. Matsen IV
Proceedings of the 34th International Conference on Machine Learning, PMLR 70:1009-1018, 2017.

Abstract

Hamiltonian Monte Carlo (HMC) is an efficient and effective means of sampling posterior distributions on Euclidean space, which has been extended to manifolds with boundary. However, some applications require an extension to more general spaces. For example, phylogenetic (evolutionary) trees are defined in terms of both a discrete graph and associated continuous parameters; although one can represent these aspects using a single connected space, this rather complex space is not suitable for existing HMC algorithms. In this paper, we develop Probabilistic Path HMC (PPHMC) as a first step to sampling distributions on spaces with intricate combinatorial structure. We define PPHMC on orthant complexes, show that the resulting Markov chain is ergodic, and provide a promising implementation for the case of phylogenetic trees in open-source software. We also show that a surrogate function to ease the transition across a boundary on which the log-posterior has discontinuous derivatives can greatly improve efficiency.

Cite this Paper

BibTeX
@InProceedings{pmlr-v70-dinh17a, title = {Probabilistic Path {H}amiltonian {M}onte {C}arlo}, author = {Vu Dinh and Arman Bilge and Cheng Zhang and Matsen, IV, Frederick A.}, booktitle = {Proceedings of the 34th International Conference on Machine Learning}, pages = {1009--1018}, year = {2017}, editor = {Precup, Doina and Teh, Yee Whye}, volume = {70}, series = {Proceedings of Machine Learning Research}, month = {06--11 Aug}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v70/dinh17a/dinh17a.pdf}, url = {https://proceedings.mlr.press/v70/dinh17a.html}, abstract = {Hamiltonian Monte Carlo (HMC) is an efficient and effective means of sampling posterior distributions on Euclidean space, which has been extended to manifolds with boundary. However, some applications require an extension to more general spaces. For example, phylogenetic (evolutionary) trees are defined in terms of both a discrete graph and associated continuous parameters; although one can represent these aspects using a single connected space, this rather complex space is not suitable for existing HMC algorithms. In this paper, we develop Probabilistic Path HMC (PPHMC) as a first step to sampling distributions on spaces with intricate combinatorial structure. We define PPHMC on orthant complexes, show that the resulting Markov chain is ergodic, and provide a promising implementation for the case of phylogenetic trees in open-source software. We also show that a surrogate function to ease the transition across a boundary on which the log-posterior has discontinuous derivatives can greatly improve efficiency.} }
Endnote
%0 Conference Paper %T Probabilistic Path Hamiltonian Monte Carlo %A Vu Dinh %A Arman Bilge %A Cheng Zhang %A Frederick A. Matsen IV %B Proceedings of the 34th International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2017 %E Doina Precup %E Yee Whye Teh %F pmlr-v70-dinh17a %I PMLR %P 1009--1018 %U https://proceedings.mlr.press/v70/dinh17a.html %V 70 %X Hamiltonian Monte Carlo (HMC) is an efficient and effective means of sampling posterior distributions on Euclidean space, which has been extended to manifolds with boundary. However, some applications require an extension to more general spaces. For example, phylogenetic (evolutionary) trees are defined in terms of both a discrete graph and associated continuous parameters; although one can represent these aspects using a single connected space, this rather complex space is not suitable for existing HMC algorithms. In this paper, we develop Probabilistic Path HMC (PPHMC) as a first step to sampling distributions on spaces with intricate combinatorial structure. We define PPHMC on orthant complexes, show that the resulting Markov chain is ergodic, and provide a promising implementation for the case of phylogenetic trees in open-source software. We also show that a surrogate function to ease the transition across a boundary on which the log-posterior has discontinuous derivatives can greatly improve efficiency.
APA
Dinh, V., Bilge, A., Zhang, C. & Matsen IV, F.A.. (2017). Probabilistic Path Hamiltonian Monte Carlo. Proceedings of the 34th International Conference on Machine Learning, in Proceedings of Machine Learning Research 70:1009-1018 Available from https://proceedings.mlr.press/v70/dinh17a.html.

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