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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].

For the entire collection see [Zbl 1154.68012].

### MSC:

68R10 | Graph theory (including graph drawing) in computer science |

### Keywords:

combined model structure; graph-separateness; interaction graph; Markovian subgraph; prime separator
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\textit{S.-H. Kim} and \textit{S. Lee}, in: 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. 116--120 (2008; Zbl 1157.68405)