Research Highlight

Posted by h.z. on September 14, 2011

message-passing on factor-graph

Partition function loop series. In a paper published in Journal of Physics A, Jing-Qing Xiao and Haijun Zhou derived the loop series expressions for the partition function and the generalized partition functions of a general graphical model. Besides obtaining the free-energy variationals used by the mean-field replica-symmetry-broken spin-glass theory, they obtained message-passing equations (belief-propagation and survey-propagation) as necessary and sufficient conditions to cancel the loop corrections of all subgraphs with dangling edges. This paper is a mathematical approach to the theory of spin-glasses. It helps to place the RSB spin-glass theory and the message-passing algorithms on a firmer mathematical ground. For the full paper, see here.