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Title: Stochastic proximal gradient algorithms for penalized mixed models Authors:  Edouard Ollier - Ecole Normale Supérieure de Lyon (France) [presenting]
Abstract: Latent variable models are classical tools to model longitudinal data such as in population pharmacokinetic with non-linear mixed effects models. Selection of such model may rely on the use of penalized maximum likelihood estimator for which penalized version of the SAEM algorithm has been developed. Even if these algorithms perform well in practice, there is a lack of theoretical information concerning their convergence. We will present convergence results in the case of a concave likelihood. Moreover, inspired from proximal gradient algorithms of deterministic optimization and Generalized EM algorithm, we will show that the M step could be reduce to a single application of a proximal gradient operator. These results will be illustrated on simulated data and on a real example.