Bibliographic Details
| 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] |
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| Database: |
Engineering Source |
