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Efficient local updates for undirected graphical models. (English) Zbl 1331.62166
Summary: We present a new Bayesian approach for undirected Gaussian graphical model determination. We provide some graph theory results for local updates that facilitate a fast exploration of the graph space. Specifically, we show how to locally update, after either edge deletion or inclusion, the perfect sequence of cliques and the perfect elimination order of the nodes associated to an oriented, directed acyclic version of a decomposable graph. Building upon the decomposable graphical models framework, we propose a more flexible methodology that extends to the class of nondecomposable graphs. Posterior probabilities of edge inclusion are interpreted as a natural measure of edge selection uncertainty. When applied to a protein expression data set, the model leads to fast estimation of the protein interaction network.

62F15 Bayesian inference
62-09 Graphical methods in statistics (MSC2010)
62M40 Random fields; image analysis
92D10 Genetics and epigenetics
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