On Fast arc-reversal

Fast arc-reversal (FAR) was recently proposed as a new exact inference algorithm in discrete Bayesian networks (BNs), merging favourable features of Arc-reversal (AR) and Variable elimination (VE). AR constantly maintains a sub-BN structure when rendering a variable barren via arc reversals, often requiring more computational effort than VE, which sacrifices a sub-BN structure by directly eliminating a variable. It was formally established that FAR can recover a unique and sound sub-BN structure after consecutive variable eliminations. Experimental results on real-world benchmark networks empirically show an improvement in the average run-time and variance of FAR compared to AR. A novel method, called d-contraction, was suggested for graphically understanding FAR since FAR is not always the same as a sequence of arc reversals. Here, we extend this work by formally establishing that AR's sub-DAG is necessarily contained within FAR's sub-DAG. Unfortunately, neither FAR nor AR can guarantee the construction of minimal I-maps, although both methods may subsequently recover minimal I-mapness. Finally, it is shown how FAR improves Sum-Product network interpretability by relaxing a restriction on the elimination ordering used.