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

arXiv: https://arxiv.org/abs/1612.04093 · HTML: https://mlsanity.com/paper/1612.04093/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 13 Dec 2016.

## Built on by (most cited first, 2 of 2)

- [Tuning diagonal scale matrices for HMC](https://mlsanity.com/paper/2403.07495/) (2024)
- [Log-density gradient covariance and automatic metric tensors for Riemann manifold Monte Carlo methods](https://mlsanity.com/paper/2211.01746/) (2022)

## Abstract (arXiv)

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