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Hamiltonian Monte C...
Hamiltonian Monte Carlo with Energy Conserving Subsampling
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- Dang, Khue-Dung (författare)
- Univ New South Wales, Australia; ARC Ctr Excellence Math and Stat Frontiers ACEMS, Australia
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- Quiroz, Matias (författare)
- ARC Ctr Excellence Math and Stat Frontiers ACEMS, Australia; Univ Technol Sydney, Australia
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- Kohn, Robert (författare)
- Univ New South Wales, Australia; ARC Ctr Excellence Math and Stat Frontiers ACEMS, Australia
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- Minh-Ngoc, Tran (författare)
- ARC Ctr Excellence Math and Stat Frontiers ACEMS, Australia; Univ Sydney, Australia
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- Villani, Mattias (författare)
- Linköpings universitet,Stockholms universitet,Statistiska institutionen,Linköping University, Sweden; ARC Centre of Excellence for Mathematical and Statistical Frontiers (ACEMS), Australia,Statistik och maskininlärning,Filosofiska fakulteten,ARC Ctr Excellence Math and Stat Frontiers ACEMS, Australia; Stockholm Univ, Sweden
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(creator_code:org_t)
- MIT Press, 2019
- 2019
- Engelska.
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Ingår i: Journal of machine learning research. - : MIT Press. - 1532-4435 .- 1533-7928. ; 20, s. 1-31
- Relaterad länk:
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http://www.jmlr.org/...
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https://liu.diva-por... (primary) (Raw object)
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https://urn.kb.se/re...
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Abstract
Ämnesord
Stäng
- Hamiltonian Monte Carlo (HMC) samples efficiently from high-dimensional posterior distributions with proposed parameter draws obtained by iterating on a discretized version of the Hamiltonian dynamics. The iterations make HMC computationally costly, especially in problems with large data sets, since it is necessary to compute posterior densities and their derivatives with respect to the parameters. Naively computing the Hamiltonian dynamics on a subset of the data causes HMC to lose its key ability to generate distant parameter proposals with high acceptance probability. The key insight in our article is that efficient subsampling HMC for the parameters is possible if both the dynamics and the acceptance probability are computed from the same data subsample in each complete HMC iteration. We show that this is possible to do in a principled way in a HMC-within-Gibbs framework where the subsample is updated using a pseudo marginal MH step and the parameters are then updated using an HMC step, based on the current subsample. We show that our subsampling methods are fast and compare favorably to two popular sampling algorithms that use gradient estimates from data subsampling. We also explore the current limitations of subsampling HMC algorithms by varying the quality of the variance reducing control variates used in the estimators of the posterior density and its gradients.
Ämnesord
- TEKNIK OCH TEKNOLOGIER -- Elektroteknik och elektronik (hsv//swe)
- ENGINEERING AND TECHNOLOGY -- Electrical Engineering, Electronic Engineering, Information Engineering (hsv//eng)
- NATURVETENSKAP -- Data- och informationsvetenskap (hsv//swe)
- NATURAL SCIENCES -- Computer and Information Sciences (hsv//eng)
- NATURVETENSKAP -- Matematik -- Sannolikhetsteori och statistik (hsv//swe)
- NATURAL SCIENCES -- Mathematics -- Probability Theory and Statistics (hsv//eng)
Nyckelord
- Bayesian inference
- Big Data
- Markov chain Monte Carlo
- Estimated likelihood
- Stochastic gradient Hamiltonian Monte Carlo
- Stochastic Gradient Langevin Dynamics
Publikations- och innehållstyp
- ref (ämneskategori)
- art (ämneskategori)
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