Prof. Eric Moulines
Dec 7th (4pm – 5pm GST)
NEO: Non-Equilibrium Sampling on the Orbit of a Deterministic Transform
Achille Thin1, Yazid Janati2, Sylvain Le Corff2, Charles Ollion1, Arnaud Doucet3, Alain Durmus4, Eric Moulines1, and Christian Robert5
1. CMAP, Ecole Polytechnique, Institut Polytechnique de Paris, Palaiseau.
2. Samovar, Telecom SudParis, Institut Polytechnique de Paris, Palaiseau.
3. Department of Statistics, University of Oxford.
4. CMLA, Ecole Normale Superieure Paris-Saclay.
5. Ceremade, Universite Paris-Dauphine & Department of Statistics, University of Warwick
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.