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Microcanonical Hamiltonian Monte Carlo.

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Title: Microcanonical Hamiltonian Monte Carlo.
Authors: Robnik, Jakob1 jakobrobnik@berkeley.edu, De Luca, G. Bruno2 gbdeluca@stanford.edu, Silverstein, Eva2 evas@stanford.edu, Seljak, Uroš3 useljak@berkeley.edu
Source: Journal of Machine Learning Research. 2023, Vol. 24, p1-34. 34p.
Subjects: Hamilton's principle function, Marginal distributions, Benchmark problems (Computer science), Canonical transformations, Bayesian field theory
Abstract: We develop Microcanonical Hamiltonian Monte Carlo (MCHMC), a class of models that follow fixed energy Hamiltonian dynamics, in contrast to Hamiltonian Monte Carlo (HMC), which follows canonical distribution with different energy levels. MCHMC tunes the Hamiltonian function such that the marginal of the uniform distribution on the constant-energy-surface over the momentum variables gives the desired target distribution. We show that MCHMC requires occasional energy-conserving billiard-like momentum bounces for ergod- icity, analogous to momentum resampling in HMC. We generalize the concept of bounces to a continuous version with partial direction preserving bounces at every step, which gives energy-conserving underdamped Langevin-like dynamics with non-Gaussian noise (MCLMC). MCHMC and MCLMC exhibit favorable scalings with condition number and dimensionality. We develop an efficient hyperparameter tuning scheme that achieves high performance and consistently outperforms NUTS HMC on several standard benchmark problems, in some cases by orders of magnitude. [ABSTRACT FROM AUTHOR]
Copyright of Journal of Machine Learning Research is the property of Microtome Publishing and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
Database: Engineering Source
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DbLabel: Engineering Source
An: 176355533
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  Data: <searchLink fieldCode="AR" term="%22Robnik%2C+Jakob%22">Robnik, Jakob</searchLink><relatesTo>1</relatesTo><i> jakobrobnik@berkeley.edu</i><br /><searchLink fieldCode="AR" term="%22De+Luca%2C+G%2E+Bruno%22">De Luca, G. Bruno</searchLink><relatesTo>2</relatesTo><i> gbdeluca@stanford.edu</i><br /><searchLink fieldCode="AR" term="%22Silverstein%2C+Eva%22">Silverstein, Eva</searchLink><relatesTo>2</relatesTo><i> evas@stanford.edu</i><br /><searchLink fieldCode="AR" term="%22Seljak%2C+Uroš%22">Seljak, Uroš</searchLink><relatesTo>3</relatesTo><i> useljak@berkeley.edu</i>
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  Data: <searchLink fieldCode="DE" term="%22Hamilton's+principle+function%22">Hamilton's principle function</searchLink><br /><searchLink fieldCode="DE" term="%22Marginal+distributions%22">Marginal distributions</searchLink><br /><searchLink fieldCode="DE" term="%22Benchmark+problems+%28Computer+science%29%22">Benchmark problems (Computer science)</searchLink><br /><searchLink fieldCode="DE" term="%22Canonical+transformations%22">Canonical transformations</searchLink><br /><searchLink fieldCode="DE" term="%22Bayesian+field+theory%22">Bayesian field theory</searchLink>
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  Label: Abstract
  Group: Ab
  Data: We develop Microcanonical Hamiltonian Monte Carlo (MCHMC), a class of models that follow fixed energy Hamiltonian dynamics, in contrast to Hamiltonian Monte Carlo (HMC), which follows canonical distribution with different energy levels. MCHMC tunes the Hamiltonian function such that the marginal of the uniform distribution on the constant-energy-surface over the momentum variables gives the desired target distribution. We show that MCHMC requires occasional energy-conserving billiard-like momentum bounces for ergod- icity, analogous to momentum resampling in HMC. We generalize the concept of bounces to a continuous version with partial direction preserving bounces at every step, which gives energy-conserving underdamped Langevin-like dynamics with non-Gaussian noise (MCLMC). MCHMC and MCLMC exhibit favorable scalings with condition number and dimensionality. We develop an efficient hyperparameter tuning scheme that achieves high performance and consistently outperforms NUTS HMC on several standard benchmark problems, in some cases by orders of magnitude. [ABSTRACT FROM AUTHOR]
– Name: AbstractSuppliedCopyright
  Label:
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  Data: <i>Copyright of Journal of Machine Learning Research is the property of Microtome Publishing and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.)
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      – Code: eng
        Text: English
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        PageCount: 34
        StartPage: 1
    Subjects:
      – SubjectFull: Hamilton's principle function
        Type: general
      – SubjectFull: Marginal distributions
        Type: general
      – SubjectFull: Benchmark problems (Computer science)
        Type: general
      – SubjectFull: Canonical transformations
        Type: general
      – SubjectFull: Bayesian field theory
        Type: general
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      – TitleFull: Microcanonical Hamiltonian Monte Carlo.
        Type: main
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            NameFull: Robnik, Jakob
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            NameFull: De Luca, G. Bruno
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            NameFull: Silverstein, Eva
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            NameFull: Seljak, Uroš
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          Dates:
            – D: 01
              M: 01
              Text: 2023
              Type: published
              Y: 2023
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              Value: 24
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            – TitleFull: Journal of Machine Learning Research
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