Hyperbolic Dirac Nets for medical decision support. Theory, methods, and comparison with Bayes Nets

We recently introduced the concept of a Hyperbolic Dirac Net (HDN) for medical inference on the grounds that, while the traditional Bayes Net (BN) is popular in medicine, it is not suited to that domain: there are many interdependencies such that any “node” can be ultimately conditional upon itself. A traditional BN is a directed acyclic graph by definition, while the HDN is a bidirectional general graph closer to a diffuse “field” of influence. Cycles require bidirectionality; the HDN uses a particular type of imaginary number from Dirac׳s quantum mechanics to encode it. Comparison with the BN is made alongside a set of recipes for converting a given BN to an HDN, also adding cycles that do not usually require reiterative methods. This conversion is called the P-method. Conversion to cycles can sometimes be difficult, but more troubling was that the original BN had probabilities needing adjustment to satisfy realism alongside the important property called “coherence”. The more general and simpler K-method, not dependent on the BN, is usually (but not necessarily) derived by data mining, and is therefore also introduced. As discussed, BN developments may converge to an HDN-like concept, so it is reasonable to consider the HDN as a BN extension.