Authors: Ilić, Velimir 
Stanković, Miomir 
Todorović, Branimir
Affiliations: Mathematical Institute of the Serbian Academy of Sciences and Arts 
Title: Computation of cross-moments using message passing over factor graphs
Journal: Advances in Mathematics of Communications
Volume: 6
Issue: 3
First page: 363
Last page: 384
Issue Date: 1-Aug-2012
Rank: M22
ISSN: 1930-5346
DOI: 10.3934/amc.2012.6.363
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.
Keywords: Commutative semiring | Cross-moment | Factor graphs | Graphical models | Message passing algorithm | Moment-generating function | Multi-index
Publisher: American Institute of Mathematical Sciences
Project: Development of new information and communication technologies, based on advanced mathematical methods, with applications in medicine, telecommunications, power systems, protection of national heritage and education 
Development of methods of computation and information processing: theory and applications 

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