Integrating integer programming and probabilistic deduction graphs for probabilistic reasoning

Optimal solutions of several variants of the probabilistic reasoning problem were found by a new technique that integrates integer programming and probabilistic deduction graphs (PDG). PDGs are extended from deduction graphs of the and-type via normal deduction graphs. The foregoing variants to be solved can involve multiple hypotheses and multiple evidences where the former is given and the latter is unknown and being found or vice versa. The relationship among these hypotheses and evidences with possible intermediaries is represented by a causal graph. The proposed method can handle a large causal graph of any type and find an optimal solution by invoking a linear integer programming package. In addition, formulating the reasoning problem to fit integer programming takes a polynomial time.