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Variational Methods and Compressed Sensing

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If you have a question about this talk, please contact Yingzhen Li.

Our focus will be to first review the compressed sensing reconstruction problem and cast it in the language of probabilistic inference. We will then show how approximate inference methods (mean-field variational inference/loopy belief propagation) can be used to derive large-scale solvers for compressed sensing reconstruction which closely resemble proximal gradient algorithms (and have connections to statistical physics). Along the way we will also explore how different forms of sparsity (l0-like spike-and-slab priors) can be naturally be incorporated into the probabilistic framework and their effect on the sparse reconstruction phase transition.

The talk will not assume prior background about compressed sensing but familiarity with graphical models and approximate inference (loopy belief propagation/variational inference) will be helpful. The talk will also be conducted using overhead slides, with a few calculations performed in detail, so having paper/pencil handy will be useful to follow along.

This talk is part of the Machine Learning Reading Group @ CUED series.

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