NEO: Non Equilibrium Sampling on the Orbit of a Deterministic Transform
This addresses challenges in Bayesian inference and statistical computing for researchers and practitioners, offering improved sampling methods with theoretical guarantees.
The paper tackles the problem of sampling from complex distributions and estimating normalizing constants by introducing NEO, a family of importance samplers and MCMC samplers based on non-equilibrium orbits of a deterministic transform, achieving state-of-the-art performance on difficult benchmarks and exploring highly multimodal targets.
Sampling from a complex distribution $π$ and approximating its intractable normalizing constant Z are challenging problems. In this paper, a novel family of importance samplers (IS) and Markov chain Monte Carlo (MCMC) samplers is derived. Given an invertible map T, these schemes combine (with weights) elements from the forward and backward Orbits through points sampled from a proposal distribution $ρ$. The map T does not leave the target $π$ invariant, hence the name NEO, standing for Non-Equilibrium Orbits. NEO-IS provides unbiased estimators of the normalizing constant and self-normalized IS estimators of expectations under $π$ while NEO-MCMC combines multiple NEO-IS estimates of the normalizing constant and an iterated sampling-importance resampling mechanism to sample from $π$. For T chosen as a discrete-time integrator of a conformal Hamiltonian system, NEO-IS achieves state-of-the art performance on difficult benchmarks and NEO-MCMC is able to explore highly multimodal targets. Additionally, we provide detailed theoretical results for both methods. In particular, we show that NEO-MCMC is uniformly geometrically ergodic and establish explicit mixing time estimates under mild conditions.