Efficient Detection of Exchangeable Factors in Factor Graphs
This work addresses a bottleneck in lifted probabilistic inference for AI/ML practitioners, offering an incremental improvement over existing methods.
The paper tackles the problem of efficiently detecting exchangeable factors in factor graphs, which is computationally expensive due to checking all permutations, and introduces the DEFT algorithm to drastically reduce this effort, validated empirically.
To allow for tractable probabilistic inference with respect to domain sizes, lifted probabilistic inference exploits symmetries in probabilistic graphical models. However, checking whether two factors encode equivalent semantics and hence are exchangeable is computationally expensive. In this paper, we efficiently solve the problem of detecting exchangeable factors in a factor graph. In particular, we introduce the detection of exchangeable factors (DEFT) algorithm, which allows us to drastically reduce the computational effort for checking whether two factors are exchangeable in practice. While previous approaches iterate all $O(n!)$ permutations of a factor's argument list in the worst case (where $n$ is the number of arguments of the factor), we prove that DEFT efficiently identifies restrictions to drastically reduce the number of permutations and validate the efficiency of DEFT in our empirical evaluation.