Constraint-Based Probabilistic Modeling for Statistical Abduction
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.
Cite
Text
Sato et al. "Constraint-Based Probabilistic Modeling for Statistical Abduction." Machine Learning, 2011. doi:10.1007/S10994-010-5206-7Markdown
[Sato et al. "Constraint-Based Probabilistic Modeling for Statistical Abduction." Machine Learning, 2011.](https://mlanthology.org/mlj/2011/sato2011mlj-constraintbased/) doi:10.1007/S10994-010-5206-7BibTeX
@article{sato2011mlj-constraintbased,
title = {{Constraint-Based Probabilistic Modeling for Statistical Abduction}},
author = {Sato, Taisuke and Ishihata, Masakazu and Inoue, Katsumi},
journal = {Machine Learning},
year = {2011},
pages = {241-264},
doi = {10.1007/S10994-010-5206-7},
volume = {83},
url = {https://mlanthology.org/mlj/2011/sato2011mlj-constraintbased/}
}