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Title: Accelerated methods for maximum likelihood estimation in mixed effects models Authors:  Belhal Karimi - INRIA Saclay - Ecole Polytechnique (France) [presenting]
Marc Lavielle - INRIA (France)
Eric Moulines - Ecole Polytechnique (France)
Abstract: Several improvements of existing methods for maximum likelihood estimation (MLE) in models with latent variables are presented. We focus on mixed effects models where the random effects are latent. In the context of nonlinear mixed effects models, the Stochastic Approximation of the EM algorithm (SAEM) is very efficient and widely used for MLE. We propose an incremental version of the SAEM that accelerates its convergence. Incremental methods have been vastly studied in the context of gradient descent type algorithms where considering a batch of points allows using bigger stepsizes and thus achieving faster convergence. We propose its extension to the SAEM. We consider an MCMC procedure for sampling the random effects and/or estimating their conditional distribution. The choice of the proposal distribution is critical mainly for multidimensional space. New techniques such as SDE-based or Hamiltonian dynamics may be efficient but are difficult to tune and are costly. We propose the use of a multidimensional Gaussian proposal that takes into account the covariance structure of the random effects we want to infer and does not require any tuning. Numerical experiments based on simulated and real data highlight the very good performances of the proposed methods.