The Inverse G-Wishart Distribution and Variational Message Passing
This work addresses a foundational problem in statistics and machine learning for researchers and practitioners developing approximate inference algorithms, but it appears incremental as it builds on existing variational message passing frameworks.
The paper tackled the challenge of expressing variational message passing factor graph fragments for approximate inference involving covariance or variance parameters, and showed that the Inverse G-Wishart distribution enables these fragments to be expressed elegantly and succinctly.
Message passing on a factor graph is a powerful paradigm for the coding of approximate inference algorithms for arbitrarily graphical large models. The notion of a factor graph fragment allows for compartmentalization 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.