Derivation of the Variational Bayes Equations
This is an incremental technical derivation that translates existing variational Bayes methods into a specific notation and extends them to Markov blanket systems.
The paper presents a detailed derivation of variational Bayes equations in Friston's notation and applies them to systems with Markov blankets, resulting in a computational framework that incorporates the 2-D cluster variation method to minimize free energy across external and representational states.
The derivation of key equations for the variational Bayes approach is well-known in certain circles. However, translating the fundamental derivations (e.g., as found in Beal's work) to Friston's notation is somewhat delicate. Further, the notion of using variational Bayes in the context of a system with a Markov blanket requires special attention. This Technical Report presents the derivation in detail. It further illustrates how the variational Bayes method provides a framework for a new computational engine, incorporating the 2-D cluster variation method (CVM), which provides a necessary free energy equation that can be minimized across both the external and representational systems' states, respectively.