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Pré-Publication, Document De Travail Année : 2017

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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Dates et versions

hal-01492056 , version 1 (17-03-2017)
hal-01492056 , version 2 (15-05-2017)
hal-01492056 , version 3 (03-08-2017)

Identifiants

  • HAL Id : hal-01492056 , version 2

Citer

Tung Duy Luu, Jalal Fadili, Christophe Chesneau. Sampling from non-smooth distribution through Langevin diffusion. 2017. ⟨hal-01492056v2⟩
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