Sparse Variational Analysis of Linear Mixed Models for Large Data Sets.

By Artin Armagan, David B. Dunson. 2011

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It is increasingly common to be faced with longitudinal or multi-level data sets that have large numbers of predictors and/or a large sample size. Current methods of fitting and inference for mixed effects models tend to perform poorly in such settings. When there are many variables, it is appealing to allow uncertainty in subset selection and to obtain a sparse characterization of the data. Bayesian methods are available to address these goals using Markov chain Monte Carlo (MCMC), but MCMC is very computationally expensive and can be infeasible in large p and/or large n problems. As a fast approximate Bayes solution, we recommend a novel approximation to the posterior relying on variational methods. Variational methods are used to approximate the posterior of the parameters in a decomposition of the variance components, with priors chosen to obtain a sparse solution that allows selection of random effects. The method is evaluated through a simulation study, and applied to an epidemiological application.

Subfields: Artificial Intelligence, Statistics and Probability

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Citations in the corpus

Variational Inference: A Review for Statisticians (2016, methodology): “ial sciences (Erosheva et al., 2007; Grimmer, 2011). General variational inference algorithms have been developed for a variety of classes of models, including shrinkage models (Armagan et al., 2011; Armagan and Dunson, 2011; Neville et al., 2014), general time-series models (Roberts et al., 2004; B”