Semiparametric regression via message passing algorithms

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Message passing algorithms are a group of fast, deterministic inference algorithms originated from the field of computer science. The focus of this thesis is on transferral of message passing algorithms into the major statistics field of semiparametric regression. We work on unveiling variational message passing (VMP) and expectation propagation (EP) from statistical perspective and developing explicit computable algorithms via VMP and EP for approximate statistical inference on model parameters in various regression models. We also contribute on demonstrating the notion of existing factor graph fragments which compartmentalise the algebra and coding required for VMP as well as developing some new fragments. We then assess the performance of VMP and EP with a Markov chain Monte Carlo (MCMC) benchmark in the context of inferential accuracy and computation speed. A series of numerical studies carried out throughout this thesis suggest that VMP and EP could be good alternatives to MCMC depending on models under consideration and the type and size of dataset.
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