A Differential Semantics of Lazy AR Propagation

In this paper we present a differential semantics of Lazy AR Propagation (LARP) in discrete Bayesian networks. We describe how both single and multi dimensional partial derivatives of the evidence may easily be calculated from a junction tree in LARP equilibrium. We show that the simplicity of the calculations stems from the nature of LARP. Based on the differential semantics we describe how variable propagation in the LARP architecture may give access to additional partial derivatives. The cautious LARP (cLARP) scheme is derived to produce a flexible cLARP equilibrium that offers additional opportunities for calculating single and multi dimensional partial derivatives of the evidence and subsets of the evidence from a single propagation. The results of an empirical evaluation illustrates how the access to a largely increased number of partial derivatives comes at a low computational cost.