NEO: Non Equilibrium Sampling on the Orbit of a Deterministic Transform

Abstract

Sampling from a complex distribution $\pi$ 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 $\rho$. The map T does not leave the target $\pi$ 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 $\pi$ while NEO-MCMC combines multiple NEO-IS estimates of the normalizing constant and an iterated sampling-importance resampling mechanism to sample from $\pi$. 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.

References in corpus (11)

• Auto-Encoding Variational Bayes
• Normalizing Flows for Probabilistic Modeling and Inference
• Bayesian Inference with Optimal Maps
• Sequential Monte Carlo smoothing for general state space hidden Markov models
• Properties of Nested Sampling
• Reinterpreting Importance-Weighted Autoencoders
• Uniform ergodicity of the Particle Gibbs sampler
• Hamiltonian Descent Methods
• Dynamical computation of the density of states and Bayes factors using nonequilibrium importance sampling
• Learning Deep Generative Models with Annealed Importance Sampling
• Unbiased Gradient Estimation for Variational Auto-Encoders using Coupled Markov Chains

Cited by in corpus (1)

• Nested sampling for physical scientists