Logical Credal Networks
- URL: http://arxiv.org/abs/2109.12240v1
- Date: Sat, 25 Sep 2021 00:00:47 GMT
- Title: Logical Credal Networks
- Authors: Haifeng Qian, Radu Marinescu, Alexander Gray, Debarun Bhattacharjya,
Francisco Barahona, Tian Gao, Ryan Riegel, Pravinda Sahu
- Abstract summary: This paper introduces Logical Credal Networks, an expressive probabilistic logic that generalizes many prior models that combine logic and probability.
We investigate its performance on maximum a posteriori inference tasks, including solving Mastermind games with uncertainty and detecting credit card fraud.
- Score: 87.25387518070411
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- Abstract: This paper introduces Logical Credal Networks, an expressive probabilistic
logic that generalizes many prior models that combine logic and probability.
Given imprecise information represented by probability bounds and conditional
probability bounds of logic formulas, this logic specifies a set of probability
distributions over all interpretations. On the one hand, our approach allows
propositional and first-order logic formulas with few restrictions, e.g.,
without requiring acyclicity. On the other hand, it has a Markov condition
similar to Bayesian networks and Markov random fields that is critical in
real-world applications. Having both these properties makes this logic unique,
and we investigate its performance on maximum a posteriori inference tasks,
including solving Mastermind games with uncertainty and detecting credit card
fraud. The results show that the proposed method outperforms existing
approaches, and its advantage lies in aggregating multiple sources of imprecise
information.
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