Modified Cholesky Riemann Manifold Hamiltonian Monte Carlo: Exploiting\n Sparsity for Fast Sampling of High-dimensional Targets

2016/12/13 by Tore Selland Kleppe, Kleppe, Tore Selland
Computer Science · Mathematics · #Bayesian Methods and Mixture Models #Computation (stat.CO) #FOS: Computer and information sciences #Gaussian Processes and Bayesian Inference #Markov Chains and Monte Carlo Methods #Methodology (stat.ME)

paper · pdf · doi:10.48550/arxiv.1612.04093

openalex publication_date 2016/12/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Riemann manifold Hamiltonian Monte Carlo (RMHMC) has the potential to produce\nhigh-quality Markov chain Monte Carlo-output even for very challenging target\ndistributions. To this end, a symmetric positive definite scaling matrix for\nRMHMC, which derives, via a modified Cholesky factorization, from the\npotentially indefinite negative Hessian of the target log-density is proposed.\nThe methodology is able to exploit the sparsity of the Hessian, stemming from\nconditional independence modeling assumptions, and thus admit fast\nimplementation of RMHMC even for high-dimensional target distributions.\nMoreover, the methodology can exploit log-concave conditional target densities,\noften encountered in Bayesian hierarchical models, for faster sampling and more\nstraight forward tuning. The proposed methodology is compared to alternatives\nfor some challenging targets, and is illustrated by applying a state space\nmodel to real data.\n

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