Computation of cross-moments using message passing over factor graphs
Velimir M. Ilić, Miomir Stanković, Branimir T. Todorović · Advances in Mathematics of Communications · 2012
This paper considers the problem of cross-moments computation forfunctions which decompose according to cycle-free factor graphs.Two algorithms are derived, both based on message passingcomputation of a corresponding moment-generating function ($MGF$).The first one is realized as message passing algorithm over apolynomial semiring and represents a computation of the $MGF$Taylor coefficients, while the second one represents messagepassing algorithm over a binomial semiring and a computation ofthe $MGF$ partial derivatives. We found that some previouslydeveloped algorithms can be seen as special cases of ouralgorithms and we consider the time and memory complexities.