Generalizing the No-U-Turn Sampler to Riemannian Manifolds

TL;DR

This paper extends the No-U-Turn Sampler (NUTS) to Riemannian Manifold Hamiltonian Monte Carlo, providing a more adaptive and efficient sampling method for complex probabilistic models.

Contribution

The paper generalizes NUTS to Riemannian manifolds, enhancing Hamiltonian Monte Carlo's adaptability and efficiency in high-dimensional spaces.

Findings

NUTS can be effectively extended to Riemannian manifolds.

The generalized NUTS improves sampling efficiency in complex models.

The dynamical basis of NUTS success is analyzed and leveraged.

Abstract

Hamiltonian Monte Carlo provides efficient Markov transitions at the expense of introducing two free parameters: a step size and total integration time. Because the step size controls discretization error it can be readily tuned to achieve certain accuracy criteria, but the total integration time is left unconstrained. Recently Hoffman and Gelman proposed a criterion for tuning the integration time in certain systems with their No U-Turn Sampler, or NUTS. In this paper I investigate the dynamical basis for the success of NUTS and generalize it to Riemannian Manifold Hamiltonian Monte Carlo.