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info.json
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{
"abstract": "We present a sound and complete graphical criterion for reading\ndependencies from the minimal undirected independence map <i>G</i> of a\ngraphoid <i>M</i> that satisfies weak transitivity. Here, complete means\nthat it is able to read all the dependencies in <i>M</i> that can be\nderived by applying the graphoid properties and weak transitivity to\nthe dependencies used in the construction of <i>G</i> and the\nindependencies obtained from <i>G</i> by vertex separation. We argue that\nassuming weak transitivity is not too restrictive. As an intermediate\nstep in the derivation of the graphical criterion, we prove that for\nany undirected graph <i>G</i> there exists a strictly positive discrete\nprobability distribution with the prescribed sample spaces that is\nfaithful to <i>G</i>. We also report an algorithm that implements the\ngraphical criterion and whose running time is considered to be at most\n<i>O</i>(<i>n</i><sup>2</sup>(<i>e</i>+<i>n</i>)) for <i>n</i> nodes \nand <i>e</i> edges. Finally, we illustrate how\nthe graphical criterion can be used within bioinformatics to identify\nbiologically meaningful gene dependencies.",
"authors": [
"Jose M. Pe{{\\~n}}a",
"Roland Nilsson",
"Johan Bj{{\\\"o}}rkegren",
"Jesper Tegn{{\\'e}}r"
],
"id": "pena09a",
"issue": 38,
"pages": [
1071,
1094
],
"title": "An Algorithm for Reading Dependencies from the Minimal Undirected Independence Map of a Graphoid that Satisfies Weak Transitivity",
"volume": "10",
"year": "2009"
}