Walk-Summable Gauss-Markov Random Fields
نویسنده
چکیده
This note introduces an interesting class of Gauss-Markov Random Fields designated as walk-summable. Several equivalent characterizations of this class of GMRFs are established. Also, several important subclasses of GMRFs are identified as being walk-summable. These include (i) diagonally dominant, (ii) pairwise normalizable, (iii) regular singly-connected, and (iv) regular bipartite with only positive (or only negative) interactions. The utility of this walk-summable property for inference of GMRFs is indicated. In particular, it is shown that several iterative estimation algorithms for GMRFs submit to a walk-sum interpretation and hence the convergence of these iterative methods is assured for walk-summable systems. Also, several interesting conjectures and ideas concerning walk-summable systems are briefly summarized in the conclusion.
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