Approximate Message Passing Algorithms for Inference and Optimization

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Message-passing algorithms are used for probabilistic inference in a variety of applications including communications, computer vision, and machine learning. Recently, there has been much interest in applying approximations of these algorithms to problems such as sparse regression and compressed sensing, where the dependence graph of the variables is dense. Despite empirical success in these settings, we do not have a sound theoretical understanding of approximate message-passing (AMP) yet. This project aims to theoretically characterize conditions under which does approximate message-passing works well. The project will also investigate applications of AMP to new settings such as capacity-achieving codes, sparse approximation, and data compression. The project is relevant to multiple EPSRC research areas including, Digital signal processing, RF and microwave communications, and Statistics and Applied probability.