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Message passing on a factor graph is a powerful paradigm for the coding ofapproximate inference algorithms for arbitrarily graphical large models. Thenotion of a factor graph fragment allows for compartmentalization of algebraand computer code. We show that the Inverse G-Wishart family of distributionsenables fundamental variational message passing factor graph fragments to beexpressed elegantly and succinctly. Such fragments arise in models for whichapproximate inference concerning covariance matrix or variance parameters ismade, and are ubiquitous in contemporary statistics and machine learning.

The Inverse G-Wishart Distribution and Variational Message Passing