Inference Methods in Pair Copula Bayesian Networks

Abstract

The aim of this thesis is the study of inference problems in Pair Copula Bayesian Networks (PCBN). To this end, certain sub-structures called arteries are identified in the PCBNs and Arterial Sample Propagation, a sample-based extension of Pearl's Belief Propagation Algorithm, is developed for single arteries. This proposed inference methodology incorporates properties unique in PCBNs as well as information on the graph structure, thus avoiding unnecessary computations and boosting the algorithm's performance. Furthermore, an extension of Arterial Sample Propagation is proposed for PCBNs with multiple arteries under some additional assumptions on the graph structure.


This thesis also explores the structural properties of PCBNs, with this examination moving in two separate directions. On the one hand we analyze inference problem reduction through pruning, building up to a pruning algorithm for PCBNs that removes a larger number of variables than existing BN pruning methods. Additionally, we study the implications that the existence of arcs in arteries have on the PCBN's structure. We prove a Theorem used as a background for Arterial Sample Propagation algorithms developed in this thesis, which has potential applications in the development stage of PCBNs.