Abstract
Abduction is one of the basic logical inferences (deduction, induction and abduction) and derives the best explanations for our observation. Statistical abduction attempts to define a probability distribution over explanations and to evaluate them by their probabilities. Logic-based probabilistic models (LBPMs) have been developed as a way to combine probabilities and logic, and it enables us to perform statistical abduction. However non-deterministic knowledge like preference and frequency seems difficult to represent by logic. Bayesian inference can reflect such knowledge on a prior distribution, and variational Bayes (VB) is known as an approximation method for it. In this paper, we propose VB for logic-based probabilistic models and show that our proposed method is efficient in evaluating abductive explanations about failure in a logic circuit and a metabolic pathway.
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Ishihata, M., Kameya, Y., Sato, T. (2012). Variational Bayes Inference for Logic-Based Probabilistic Models on BDDs. In: Muggleton, S.H., Tamaddoni-Nezhad, A., Lisi, F.A. (eds) Inductive Logic Programming. ILP 2011. Lecture Notes in Computer Science(), vol 7207. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-31951-8_19
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DOI: https://doi.org/10.1007/978-3-642-31951-8_19
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