An Efficient Implementation of Riemannian Manifold Hamiltonian Monte Carlo for Gaussian Process Models
This work addresses computational bottlenecks for researchers and practitioners in Bayesian statistics and machine learning, but it is incremental as it focuses on implementation details rather than new theoretical insights.
The authors tackled the problem of efficiently sampling from high-dimensional posterior distributions in Gaussian Process models by presenting a detailed implementation of Riemannian manifold Hamiltonian Monte Carlo, resulting in a method that provides sufficient technical and algorithmic details for practical use.
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.