Sampling from non-smooth distribution through Langevin diffusion
Résumé
In this paper, we propose proximal splitting-type algorithms for sampling from distributions whose
densities are not necessarily smooth nor log-concave. Our approach brings together tools from, on the
one hand, variational analysis and non-smooth optimization, and on the other hand, stochastic diffusion
equations, and in particular the Langevin diffusion. We establish in particular consistency guarantees
of our algorithms seen as discretization schemes in this context. These algorithms are then applied to
compute the exponentially weighted aggregates for regression problems involving non-smooth priors
encouraging some notion of simplicity/complexity. Some popular priors are detailed and implemented
on some numerical experiments.
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