Bayesian Inference and Optimal Design in the Sparse Linear Model
matthias seeger, Florian Steinke and Koji Tsuda
In: Workshop on AI and Statistics, Puerto Rico(2007).

Abstract

The sparse linear model has seen many successful applications in Statistics, Machine Learning, and Computational Biology, such as identification of gene regulatory networks from micro-array expression data, or sparse coding of images with overcomplete basis sets. Prior work has either approximated Bayesian inference by expensive Markov chain Monte Carlo, or replaced it by point estimation. We show how to obtain a good approximation to Bayesian analysis efficiently, using the Expectation Propagation method. We also address problems of optimal design and hyperparameter estimation, motivating their use in several practical problems.

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