Elicitation, estimation and exact inference in Bayesian Networks (BNs) are often difficult because the dimension of eachConditional Probability Table (CPT) grows exponentially with the increase in the number of parent variables. The NoisyMAX decomposition has been proposed to break down a large CPT into several smaller CPTs exploiting the assumptionof causal independence, i.e., absence of causal interaction among parent variables. In this way, the number of conditionalprobabilities to be elicited or estimated and the computational burden of the joint tree algorithm for exact inference arereduced. Unfortunately, the Noisy-MAX decomposition is suited to graded variables only, i.e., ordinal variables with thelowest state as reference, but real-world applications of BNs may also involve a number of non-graded variables, like theones with reference state in the middle of the sample space (double-graded variables) and with two or more unorderednon-reference states (multi-valued nominal variables). In this paper, we propose the causal independence decomposition,which includes the Noisy-MAX and two generalizations suited to double-graded and multi-valued nominal variables.While the general definition of BN implicitly assumes the presence of all the possible causal interactions, our proposal isbased on causal independence, and causal interaction is a feature that can be added upon need. The impact of our proposalis investigated on a published BN for the diagnosis of acute cardiopulmonary diseases.
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