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In this paper, an exact bitwise MAP (Maximum A Posteriori) estimationalgorithm for group testing problems is presented. We assume a simplestnon-adaptive group testing scenario including N-objects with binary status andM-disjunctive tests. If a group contains a positive object, the test result forthe group is assumed to be one; otherwise, the test result becomes zero. Ourinference problem is to evaluate the posterior probabilities of the objectsfrom the observation of M-test results and from our knowledge on the priorprobabilities for objects. The heart of the algorithm is the dual expression ofthe posterior values. The derivation of the dual expression can be naturallydescribed based on a holographic transformation to the normal factor graph(NFG) representing the inference problem.

Bitwise MAP Algorithm for Group Testing based on Holographic Transformation