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Abstract

Expectation propagation (EP) is a novel variational method for approximate Bayesian inference, which has given promising results in terms of computational efficiency and accuracy in several machine learning applications. It can readily be applied to inference in linear models with non-Gaussian priors, generalised linear models, or nonparametric Gaussian process models, among others. I will give an introduction to this framework. Important aspects of EP are not well-understood theoretically. I will highlight some open problems.

I will then show how to address sequential experimental design for a linear model with non-Gaussian sparsity priors, giving some results in two different machine learning applications. These results indicate that experimental design for these models may have significantly different properties than for linear-Gaussian models, where Bayesian inference is analytically tractable and experimental design seems best understood.