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Erschienen in:
Minimizing Regret in Dynamic Decision Problems Kapitel lesen Erstes Kapitel lesen

2015 | OriginalPaper | Buchkapitel

Every LWF and AMP Chain Graph Originates from a Set of Causal Models

verfasst von : Jose M. Peña

Erschienen in: Symbolic and Quantitative Approaches to Reasoning with Uncertainty

Verlag: Springer International Publishing

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Abstract

This paper aims at justifying LWF and AMP chain graphs by showing that they do not represent arbitrary independence models. Specifically, we show that every chain graph is inclusion optimal wrt the intersection of the independence models represented by a set of directed and acyclic graphs under conditioning. This implies that the independence model represented by the chain graph can be accounted for by a set of causal models that are subject to selection bias, which in turn can be accounted for by a system that switches between different regimes or configurations.

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Vorheriges Kapitel Evaluating Product-Based Possibilistic Networks Learning Algorithms
Nächstes Kapitel Factorization, Inference and Parameter Learning in Discrete AMP Chain Graphs
Fußnoten
1
Unfortunately, we could not get access to this work. So, we trust the description of it made in [25, Sect 3.5].
 
2
See [17, Remark 3.1] for the equivalence of this and the standard definition of Z-open route for AMP CGs.
 
3
Note that \(de_{G_{\alpha }}(X)\) for any \(X \in b_i\) is known when the second step for \(b_i\) starts, because \(ne_{G_{\alpha }}(X)\) for any \(X \in \bigcup _{j=i}^{n} b_j\) and \(pa_{G_{\alpha }}(X)\) for any \(X \in \bigcup _{j=i+1}^{n} b_j\) have already been identified.
 
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Metadaten
Titel
Every LWF and AMP Chain Graph Originates from a Set of Causal Models
verfasst von
Jose M. Peña
Copyright-Jahr
2015
Buch
Symbolic and Quantitative Approaches to Reasoning with Uncertainty

Print ISBN: 978-3-319-20806-0

Electronic ISBN: 978-3-319-20807-7

Copyright-Jahr: 2015

DOI
https://doi.org/10.1007/978-3-319-20807-7_29