Applications of approximate inference and experimental design for sparse (generalised) linear models
Seminar Room 1, Newton Institute
Sparsity, or more general sub-Gaussianity, is a fundamental regularization principle for high-dimensional statistics. A recent surge of activity has clarified the behaviour of efficient sparse estimators in the worst case, but much less is known about practically efficient approximations to Bayesian inference, which is required for higher-level tasks such as experimental design.
We present an efficient framework for Bayesian inference on generalized linear models with sparsity priors, based on the expectation propagation algorithm, a deterministic variational approximation. We highlight some applications where this framework produces promising results. We hope to convey the relevance of approximate inference methods in practice, which substantially go beyond point estimation, yet whose theoretical properties and algorithmic scalability remains insufficiently understood.
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