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Title: Compartmentalisation of variational approximate inference for inverse problems models Authors:  Luca Maestrini - The Australian National University (Australia) [presenting]
Robert G Aykroyd - University of Leeds (United Kingdom)
Matt P Wand - University of Technology Sydney (Australia)
Abstract: Inverse problems are essentially statistical regression problems where a response depending on a number of causal factors or parameters is measured and the goal is to estimate the parameter values. However, they may be highly multivariate and have predictors which are highly correlated. Hence even linear inverse problems cannot be solved by classical regression methods, nor can they be solved using standard dimension reduction or regularised regression techniques. A remedy is to use Markov random field models, which can be slow to fit via Markov chain Monte Carlo methods. Variational message passing updating algorithms for factor graph fragments arising in inverse problem Bayesian models are identified, catalogued and derived. The resultant factor graph fragments facilitate streamlined implementation of fast approximate algorithms for inverse problems and form the basis for software development. Contemporary inverse problems models give rise to new factor graph fragment types for different penalization strategies. Nevertheless, the variational message passing approach on factor graph fragments is such that algorithm updates and streamlining steps only need to be derived once for a particular fragment, which can be integrated in an arbitrarily complex model. The first applications are one- and two-dimensional deconvolution problems motivated by archaeology data.