  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.
