Sampling from non-smooth distribution through Langevin diffusion

Tung Duy Luu (1) , Jalal Fadili (1) , Christophe Chesneau (2)

1 Equipe Image - Laboratoire GREYC - UMR6072
2 LMNO - Laboratoire de Mathématiques Nicolas Oresme

In this paper, we propose algorithms for sampling from the distributions whose density is non-smoothed nor log-concave. Our algorithms are based on the Langevin diffusion on the regularized counterpart of density by the Moreau-Yosida regularization. These results are then applied to compute the exponentially weighted aggregates for high dimensional framework with a general class of priors encouraging objects which conform to some notion of simplicity/complexity. Some popular priors are detailed and implemented on some numerical experiments.

Domaines: Statistiques [math.ST]

Tung Duy Luu, Jalal Fadili, Christophe Chesneau. Sampling from non-smooth distribution through Langevin diffusion. 2017. ⟨hal-01492056v1⟩