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Gradient-based Adaptive Markov Chain Monte Carlo

Dellaportas, P; Titsias, M; (2019) Gradient-based Adaptive Markov Chain Monte Carlo. In: Proceedings of the 33rd Conference on Neural Information Processing Systems (NeurIPS 2019). 33rd Conference on Neural Information Processing Systems (NeurIPS 2019): Vancouver, Canada. Green open access

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Abstract

We introduce a gradient-based learning method to automatically adapt Markov chain Monte Carlo (MCMC) proposal distributions to intractable targets. We define a maximum entropy regularised objective function, referred to as generalised speed measure, which can be robustly optimised over the parameters of the proposal distribution by applying stochastic gradient optimisation. An advantage of our method compared to traditional adaptive MCMC methods is that the adaptation occurs even when candidate state values are rejected. This is a highly desirable property of any adaptation strategy because the adaptation starts in early iterations even if the initial proposal distribution is far from optimum. We apply the framework for learning multivariate random walk Metropolis and Metropolis-adjusted Langevin proposals with full covariance matrices, and provide empirical evidence that our method can outperform other MCMC algorithms, including Hamiltonian Monte Carlo schemes.

Type: Proceedings paper
Title: Gradient-based Adaptive Markov Chain Monte Carlo
Event: 33rd Conference on Neural Information Processing Systems (NeurIPS 2019)
Location: Vancouver, Canada
Dates: 09 December 2019 - 14 December 2019
Open access status: An open access version is available from UCL Discovery
Publisher version: https://papers.nips.cc/paper/9703-gradient-based-a...
Language: English
Additional information: This version is the version of record. For information on re-use, please refer to the publisher’s terms and conditions.
UCL classification: UCL
UCL > Provost and Vice Provost Offices
UCL > Provost and Vice Provost Offices > UCL BEAMS
UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences
UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences > Dept of Statistical Science
URI: https://discovery.ucl.ac.uk/id/eprint/10081211
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