Sampling from non-smooth distribution through Langevin diffusion

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

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

In this paper, we propose proximal splitting-type algorithms for sampling from distributions whosedensities are not necessarily smooth nor log-concave. Our approach brings together tools from, on theone hand, variational analysis and non-smooth optimization, and on the other hand, stochastic diffusionequations, and in particular the Langevin diffusion. We establish in particular consistency guaranteesof our algorithms seen as discretization schemes in this context. These algorithms are then applied tocompute the exponentially weighted aggregates for regression problems involving non-smooth priorsencouraging some notion of simplicity/complexity. Some popular priors are detailed and implementedon some numerical experiments.

Mots clés: Regression model; Langevin diffusion; Penalized estimators; Exponential weighted aggregation

Domaines: Statistiques [math.ST]

Duy Tung Luu, Jalal M. Fadili, Christophe Chesneau. Sampling from non-smooth distribution through Langevin diffusion. 2017. ⟨hal-01492056v3⟩