2022/12/16 by Jakob Robnik, G. Bruno De Luca, Robnik, Jakob +5 · 6 citations
Biochemistry, Genetics and Molecular Biology · Mathematics · Physics and Astronomy · #Computation (stat.CO) #FOS: Computer and information sciences #FOS: Physical sciences #High Energy Physics - Lattice (hep-lat) #High Energy Physics - Theory (hep-th) #Instrumentation and Methods for Astrophysics (astro-ph.IM) #Markov Chains and Monte Carlo Methods #Protein Structure and Dynamics #Statistical Mechanics and Entropy
paper · pdf · doi:10.48550/arxiv.2212.08549
openalex publication_date 2022/12/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/30
We develop Microcanonical Hamiltonian Monte Carlo (MCHMC), a class of models which follow a 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 ergodicity, 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 an 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 more than an order of magnitude.