2023/01/04 by James A. Brofos, Brofos, James A., Vivekananda Roy +3
Computer Science · Mathematics · Physics and Astronomy · #Computation (stat.CO) #FOS: Computer and information sciences #Gaussian Processes and Bayesian Inference #Machine Learning (stat.ML) #Markov Chains and Monte Carlo Methods #Methodology (stat.ME) #Model Reduction and Neural Networks
paper · pdf · doi:10.48550/arxiv.2301.01409
openalex publication_date 2023/01/04 · openalex created_date 2023/01/06 · openalex updated_date 2026/08/01
Riemannian manifold Hamiltonian (RMHMC) and Lagrangian Monte Carlo (LMC) have emerged as powerful methods of Bayesian inference. Unlike Euclidean Hamiltonian Monte Carlo (EHMC) and the Metropolis-adjusted Langevin algorithm (MALA), the geometric ergodicity of these Riemannian algorithms has not been extensively studied. On the other hand, the manifold Metropolis-adjusted Langevin algorithm (MMALA) has recently been shown to exhibit geometric ergodicity under certain conditions. This work investigates the mixture of the LMC and RMHMC transition kernels with MMALA in order to equip the resulting method with an "inherited" geometric ergodicity theory. We motivate this mixture kernel based on an analogy between single-step HMC and MALA. We then proceed to evaluate the original and modified transition kernels on several benchmark Bayesian inference tasks.