2022/06/14 by Geoffrey McGregor, McGregor, Geoffrey, Andy T. S. Wan +1
Mathematics · #Computation (stat.CO) #FOS: Computer and information sciences #FOS: Mathematics #Markov Chains and Monte Carlo Methods #Mathematical Approximation and Integration #Methodology (stat.ME) #Numerical Analysis (math.NA) #Statistical Methods and Inference
paper · pdf · doi:10.48550/arxiv.2206.06901
openalex publication_date 2022/06/14 · openalex created_date 2022/06/17 · openalex updated_date 2026/07/28
Hamiltonian Monte Carlo is a prominent Markov Chain Monte Carlo algorithm, which employs symplectic integrators to sample from high dimensional target distributions in many applications, such as statistical mechanics, Bayesian statistics and generative models. However, such distributions tend to have thin high density regions, posing a significant challenge for symplectic integrators to maintain the small energy errors needed for a high acceptance probability. Instead, we propose a variant called Conservative Hamiltonian Monte Carlo, using R--reversible energy-preserving integrators to retain a high acceptance probability. We show our algorithm can achieve approximate stationarity with an error determined by the Jacobian approximation of the energy-preserving proposal map. Numerical evidence shows improved convergence and robustness over integration parameters on target distributions with thin high density regions and in high dimensions. Moreover, a version of our algorithm can also be applied to target distributions without gradient information.