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Abstract:
Sparse linear models are cornerstones of applied statistics, embodying fundamental ideas
such as feature selection, shrinkage, and automatic relevance determination. While much
progress has been made recently in understanding point estimation of sparse signals, Bayesian
inference is needed to drive higher-level tasks such as experimental design, where valid un-
certainties and covariances are more important than point estimates. In this tutorial, the ma-
jor determnistic inference approximations to date (expectation propagation, sparse Bayesian
learning, variational mean field Bayes) will be introduced for the sparse linear model, and
their mathematics (scale mixtures, convex duality, moment matching) will be clarified. Se-
quential Bayesian design, with the application to optimizing an image measurement archi-
tecture, serves as motivation for this effort.
