dc.contributor.author Salim, Adil dc.contributor.author Korba, Anna dc.contributor.author Luise, Giulia dc.date.accessioned 2020-02-27T05:42:22Z dc.date.available 2020-02-27T05:42:22Z dc.date.issued 2020-02-07 dc.identifier.uri http://hdl.handle.net/10754/661742 dc.description.abstract We consider the task of sampling from a log-concave probability distribution. This target distribution can be seen as a minimizer of the relative entropy functional defined on the space of probability distributions. The relative entropy can be decomposed as the sum of a functional called the potential energy, assumed to be smooth, and a nonsmooth functional called the entropy. We adopt a Forward Backward (FB) Euler scheme for the discretization of the gradient flow of the relative entropy. This FB algorithm can be seen as a proximal gradient algorithm to minimize the relative entropy over the space of probability measures. Using techniques from convex optimization and optimal transport, we provide a non-asymptotic analysis of the FB algorithm. The convergence rate of the FB algorithm matches the convergence rate of the classical proximal gradient algorithm in Euclidean spaces. The practical implementation of the FB algorithm can be challenging. In practice, the user may choose to discretize the space and work with empirical measures. In this case, we provide a closed form formula for the proximity operator of the entropy. dc.publisher arXiv dc.relation.url https://arxiv.org/pdf/2002.03035 dc.rights Archived with thanks to arXiv dc.title Wasserstein Proximal Gradient dc.type Preprint dc.contributor.department Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division dc.contributor.department Visual Computing Center (VCC) dc.eprint.version Pre-print dc.contributor.institution Gatsby Computational Neuroscience Unit, University College London dc.contributor.institution Computer Science Department, University College London dc.identifier.arxivid arXiv:2002.03035 kaust.person Salim, Adil refterms.dateFOA 2020-02-27T05:42:46Z
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