NeurIPS 2022

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Poster

Logical Credal Networks

Radu Marinescu · Haifeng Qian · Alexander Gray · Debarun Bhattacharjya · Francisco Barahona · Tian Gao · Ryan Riegel · Pravinda Sahu

Wed Nov 30 09:00 AM -- 11:00 AM (PST) @ Hall J #801

in Poster Session 3 »

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.

Keywords: Graphical Models · probabilistic logic · knowledge representation · bayesian networks

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Author Information

Radu Marinescu (IBM Research)

Haifeng Qian (Amazon AWS AI Labs)

Alexander Gray (International Business Machines)

Debarun Bhattacharjya (IBM Research)

Francisco Barahona (IBM Research AI)

Tian Gao (IBM Research)

Ryan Riegel (IBM Research)

Ryan Riegel is a researcher in the AI Reasoning group at IBM Research. He works on neuro-symbolic reasoning methods and their related technologies, including sound and complete real-valued logic, logically constrained neural network learning, extensions of said to temporal and modal logic, and applications including natural language question answering. In the past, he has worked on fast algorithms for a family of nonparametric machine learning methods dubbed generalized N-Body problems, which includes all-nearest-neighbors and kernel density estimation. He also co-founded an AI startup where he oversaw and contributed to the development of enterprise-grade machine learning software for Big Data. He received a Joint BS in Mathematics and Computer Science from Harvey Mudd College and a PhD in Computer Science from the Georgia Institute of Technology.