Logical Credal Networks
Radu Marinescu, Haifeng Qian, Alexander G. Gray, Debarun Bhattacharjya, Francisco Barahona, Tian Gao, Ryan Riegel, Pravinda Sahu
Abstract
We introduce Logical Credal Networks (or LCNs for short) -- an expressive probabilistic logic that generalizes prior formalisms that combine logic and probability. Given imprecise information represented by probability bounds and conditional probability bounds on logic formulas, an LCN specifies a set of probability distributions over all its interpretations. Our approach allows propositional and first-order logic formulas with few restrictions, e.g., without requiring acyclicity. We also define a generalized Markov condition that allows us to identify implicit independence relations between atomic formulas. We evaluate our method on benchmark problems such as random networks, Mastermind games with uncertainty and credit card fraud detection. Our results show that the LCN outperforms existing approaches; its advantage lies in aggregating multiple sources of imprecise information.
BibTeX
@inproceedings{
marinescu2022logical,
title={Logical Credal Networks},
author={Radu Marinescu and Haifeng Qian and Alexander G. Gray and Debarun Bhattacharjya and Francisco Barahona and Tian Gao and Ryan Riegel and Pravinda Sahu},
booktitle={Advances in Neural Information Processing Systems},
editor={Alice H. Oh and Alekh Agarwal and Danielle Belgrave and Kyunghyun Cho},
year={2022},
url={https://openreview.net/forum?id=wiGXs_kS_X}
}