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A model searching method based on marginal model stuctures. (English) Zbl 1157.68405
Gammerman, A. (ed.), Artificial intelligence and applications. Machine learning. As part of the 26th IASTED international multi-conference on applied informatics. Calgary: International Association of Science and Technology for Development (IASTED); Anaheim, CA: Acta Press (ISBN 978-0-88986-710-9/CD-ROM). 116-120 (2008).
Summary: Suppose that we are interested in modeling for a random vector $$X$$ and that we are given a set of graphical decomposable models,$$\mathcal{G}_1,\dots,\mathcal{G}_m$$, for subvectors of $$X$$ each of which share some variables with at least one of the other models. Under the assumption that the model of $$X$$ is graphical and decomposable, we propose an approach of searching for models of $$X$$ based on the given decomposable graphical models. A main idea in this approach is that we combine $$\mathcal{G}_1,\dots,\mathcal{G}_m$$ using graphs of prime separators (section 2). When the true graphical model for the whole data is decomposable, prime separators in a marginal model are also prime separators in a maximal combined model of the marginal models. This property plays a key role in model-combination. The proposed approach is applied to searching for a model of 100 variables for illustration.
For the entire collection see [Zbl 1154.68012].

##### MSC:
 68R10 Graph theory (including graph drawing) in computer science