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Variational learning for rectified factor analysis
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Variational approximations in Bayesian model selection for finite mixture distributions
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Building Blocks for Variational Bayesian Learning of Latent Variable Models
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Dynamic hierarchical Markov random fields and their application to web data extraction
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Blind separation of nonlinear mixtures by variational Bayesian learning
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Efficiently Learning Random Fields for Stereo Vision with Sparse Message Passing
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Mean field approach for tracking similar objects
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Message family propagation for ising mean field based on iteration tree
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Hidden Markov models with stick-breaking priors
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Sided and symmetrized Bregman centroids
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A Study on Smoothing for Particle-Filtered 3D Human Body Tracking
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Adaptive iterative detectors for phase-uncertain channels via variational bounding
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Robust Bayesian mixture modelling
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On Learning Conditional Random Fields for Stereo
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Gaussian message propagation in d-order neighborhood for gaussian graphical model
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Bayesian inference is now widely established as one of the principal foundations for machine learning. In practice, exact inference is rarely possible, and so a variety of approximation techniques have been developed, one of the most widely used being a deterministic framework called variational inference. In this paper we introduce Variational Message Passing (VMP), a general purpose algorithm for applying variational inference to Bayesian Networks. Like belief propagation, VMP proceeds by sending messages between nodes in the network and updating posterior beliefs using local operations at each node. Each such update increases a lower bound on the log evidence (unless already at a local maximum). In contrast to belief propagation, VMP can be applied to a very general class of conjugate-exponential models because it uses a factorised variational approximation. Furthermore, by introducing additional variational parameters, VMP can be applied to models containing non-conjugate distributions. The VMP framework also allows the lower bound to be evaluated, and this can be used both for model comparison and for detection of convergence. Variational message passing has been implemented in the form of a general purpose inference engine called VIBES ('Variational Inference for BayEsian networkS') which allows models to be specified graphically and then solved variationally without recourse to coding.