A Bayesian network (BN) is a probabilistic graphical model representing causal dependence and conditional independence among domain variables. The strength of dependence is quantified by conditional probability tables (CPTs). The space complexity of BNs is exponential on the number of parents per variable, which limits the effectiveness of knowledge acquisition and inference. Non-impeding noisy-AND tree (NAT) models give a highly expressive approximate representation of BNs. Approximating CPTs in BNs by NAT models can significantly reduce the space complexity and speed up BN inference. In this thesis, we generalize the CPT approximation by NAT models. Leaky causes, representing all causes that are not explicitly modeled, exist in CPTs from real world BNs. We approximate CPTs with persistent leaky causes (PLCs) by explicitly modeling such leaky causes. Experimental results show that approximating general CPTs by NAT models is reasonably accurate. Explicitly modeling PLCs further improves the accuracy in CPTs with PLCs.