# American Institute of Mathematical Sciences

August  2012, 6(3): 363-384. doi: 10.3934/amc.2012.6.363

## Computation of cross-moments using message passing over factor graphs

 1 Mathematical Institute of the Serbian Academy of Sciences and Arts, Kneza Mihaila 36, 11000 Beograd, Serbia 2 University of Niš, Faculty of Occupational Safety, Čarnojevića 10a, 18000 Niš, Serbia, Serbia

Received  November 2011 Revised  May 2012 Published  August 2012

This paper considers the problem of cross-moments computation for functions which decompose according to cycle-free factor graphs. Two algorithms are derived, both based on message passing computation of a corresponding moment-generating function ($MGF$). The first one is realized as message passing algorithm over a polynomial semiring and represents a computation of the $MGF$ Taylor coefficients, while the second one represents message passing algorithm over a binomial semiring and a computation of the $MGF$ partial derivatives. We found that some previously developed algorithms can be seen as special cases of our algorithms and we consider the time and memory complexities.
Citation: Velimir M. Ilić, Miomir S. Stanković, Branimir T. Todorović. Computation of cross-moments using message passing over factor graphs. Advances in Mathematics of Communications, 2012, 6 (3) : 363-384. doi: 10.3934/amc.2012.6.363
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