Breadcrumb
Proximal Markov chain Monte Carlo: non-smooth convex optimisation and stochastic simulation.
Fri 17 May 2013, 14:15
Marcelo Pereyra
Bristol
Organisers: Nick Whiteley, Feng Yu
ABSTRACT
This talk presents three new Metropolis-Hastings algorithms to simulate samples from very high-dimensional concave distributions that are not smooth, a class of models that is key to modern signal processing, machine learning and sparse statistics. Performing inference on these models is challenging and currently receives a lot of attention in the non-smooth convex optimisation literature. The methods presented in this talk combine non-smooth convex optimisation with MCMC and generalise the Metropolis adjusted Lanvegin algorithm to a wide range of non-differentiable distributions. This is achieved by considering discretizations of Langevin diffusions associated with smooth Moreau approximations of the target density. The resulting algorithms exploit the proximity mappings (generalised projection operators) of the target density to efficiently explore the parameter space. The proposed methodology is demonstrated on high-dimensional LASSO and low-rank matrix denoising models.