Empirical Bayes for high-dimensional prediction
schedule le mardi 23 octobre 2018 de 10h45 à 11h45
Organisé par : Castillo, Fischer, Giulini, Gribkova, Levrard, Roquain, Sangnier
Intervenant : Mark van de Wiel (VU Amsterdam)
Lieu : UPMC, salle 15-16.201
Sujet : Empirical Bayes for high-dimensional prediction
Empirical Bayes enables “learning from a lot” in two ways: first, from a large number of variables and second, from a potentially large amount of prior information on the variables, termed ‘co-data’. We discuss empirical Bayes methods for estimating hyperparameters (e.g. penalties) in regression-based prediction models, such as spike-and-slab, the elastic net and ridge. For the latter, some theoretical results are presented for the quality of an empirical Bayes estimator in terms of n and p.Empirical Bayes is particularly useful to estimate multiple hyper-parameters that model the information in the co-data. Some examples of co-data are: p-values from an external study, additional molecular measurements or genomic annotation. For spike-and-slab and elastic net regression we illustrate how to apply empirical Bayes in the co-data setting when only posterior approximations are available (e.g. provided by MCMC or variational Bayes). The systematic use of co-data can considerably improve predictions and variable selection, which we demonstrate on a cancer genomics application.