The Inverse G-Wishart distribution and variational message passing

Message passing on a factor graph is a powerful paradigm for the coding of approximate inference algorithms for arbitrarily large graphical models. The notion of a factor graph fragment allows for compartmentalisation of algebra and computer code. We show that the Inverse G-Wishart family of distributions enables fundamental variational message passing factor graph fragments to be expressed elegantly and succinctly. Such fragments arise in models for which approximate inference concerning covariance matrix or variance parameters is made, and are ubiquitous in contemporary statistics and machine learning.