Deterministic Gibbs Sampling via Ordinary Differential Equations
This work provides a general framework for deterministic MCMC sampling, which is incremental but offers improved efficiency for practitioners in computational statistics and machine learning.
The paper tackles the problem of constructing deterministic, measure-preserving dynamics for MCMC sampling using autonomous ODEs and differential geometry, resulting in deterministic samplers that are more sample efficient than stochastic counterparts, even when the latter generate independent samples.
Deterministic dynamics is an essential part of many MCMC algorithms, e.g. Hybrid Monte Carlo or samplers utilizing normalizing flows. This paper presents a general construction of deterministic measure-preserving dynamics using autonomous ODEs and tools from differential geometry. We show how Hybrid Monte Carlo and other deterministic samplers follow as special cases of our theory. We then demonstrate the utility of our approach by constructing a continuous non-sequential version of Gibbs sampling in terms of an ODE flow and extending it to discrete state spaces. We find that our deterministic samplers are more sample efficient than stochastic counterparts, even if the latter generate independent samples.