An Efficient Implementation of Riemannian Manifold Hamiltonian Monte Carlo for Gaussian Process Models

TL;DR

This paper introduces an efficient implementation of Riemannian Manifold Hamiltonian Monte Carlo tailored for Gaussian Process models, providing detailed pseudo-code and algorithms to facilitate sampling from complex posterior distributions.

Contribution

The paper offers a specialized, computationally efficient implementation of RMHMC for Gaussian Process models, including detailed pseudo-code and algorithmic guidance.

Findings

Enhanced sampling efficiency for GP posteriors

Detailed pseudo-code for practical implementation

Improved computational performance over previous methods

Abstract

This technical report presents pseudo-code for a Riemannian manifold Hamiltonian Monte Carlo (RMHMC) method to efficiently simulate samples from $N$-dimensional posterior distributions $p(x|y)$, where $x \in R^N$ is drawn from a Gaussian Process (GP) prior, and observations $y_n$ are independent given $x_n$. Sufficient technical and algorithmic details are provided for the implementation of RMHMC for distributions arising from GP priors.