Constraint-based probabilistic modeling for statistical abduction |
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Authors: | Taisuke Sato Masakazu Ishihata Katsumi Inoue |
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Affiliation: | (1) Tokyo Institute of Technology, Ookayama Meguro, Tokyo, Japan |
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Abstract: | We introduce a new framework for logic-based probabilistic modeling called constraint-based probabilistic modeling which defines CBPMs (constraint-based probabilistic models) , i.e. conditional joint distributions P(⋅∣KB) over independent propositional variables constrained by a knowledge base KB consisting of clauses. We first prove that generative models such as PCFGs and discriminative models such as CRFs have equivalent
CBPMs as long as they are discrete. We then prove that CBPMs in infinite domains exist which give existentially closed logical
consequences of KB probability one. Finally we derive an EM algorithm for the parameter learning of CBPMs and apply it to statistical abduction. |
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