On the Detection of Commutative Factors in Factor Graphs: Necessary and Sufficient Conditions
The paper discusses the detection of commutative factors in factor graphs, which are essential for efficient probabilistic inference. It critiques the current state-of-the-art algorithm, highlighting a flaw in its reliance on a theorem that is misinterpreted as a sufficient condition. The authors propose a corrected theorem and an improved algorithm that maintains efficiency while ensuring accuracy in identifying commutative factors.
- ▪The paper addresses the identification of commutative factors in factor graphs, crucial for lifted probabilistic inference.
- ▪It reveals that the existing algorithm is based on a misinterpreted theorem, leading to potentially incorrect results.
- ▪The authors provide a modified theorem and a new algorithm that corrects the flaws while preserving efficiency.
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Computer Science > Artificial Intelligence arXiv:2605.26908 (cs) [Submitted on 26 May 2026] Title:On the Detection of Commutative Factors in Factor Graphs: Necessary and Sufficient Conditions Authors:Malte Luttermann, Ralf Möller, Marcel Gehrke View a PDF of the paper titled On the Detection of Commutative Factors in Factor Graphs: Necessary and Sufficient Conditions, by Malte Luttermann and 2 other authors View PDF Abstract:Exploiting the indistinguishability of objects in a probabilistic graphical model such as a factor graph is key to lifted probabilistic inference algorithms and allows for tractable probabilistic inference problems with respect to domain sizes.
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