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Eric Moulines

 

Wednesday 24th February 2016

Time: 4.00pm

 

Ground Floor Seminar Room

25 Howland Street, London, W1T 4JG

 

Sampling from log-concave non-smooth densities, when Moreau meets Langevin

 

In this talk, a new algorithm to sample from possibly non-smooth 
log-concave probability measures is introduced. This algorithm uses 
Moreau-Yosida envelope combined with the Euler-Maruyama discretization 
of Langevin diffusions. They are applied to a deconvolution problem in 
image processing, which shows that they can be practically used in a 
high dimensional setting. Finally, non-asymptotic convergence bounds (in 
total variation and wasserstein distances) are derived. These bounds 
follow from non-asymptotic results for ULA applied to probability 
measures with a continuously differentiable log-concave density. [A 
paper will be arxived soon (updating http://arxiv.org/abs/1507.05021).]