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Learning AMP Chain Graphs under Faithfulness
 SIXTH EUROPEAN WORKSHOP ON PROBABILISTIC GRAPHICAL MODELS, GRANADA, SPAIN, 2012
, 2012
"... This paper deals with chain graphs under the alternative AnderssonMadiganPerlman (AMP) interpretation. In particular, we present a constraint based algorithm for learning an AMP chain graph a given probability distribution is faithful to. We also show that the extension of Meek’s conjecture to AMP ..."
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Cited by 4 (4 self)
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This paper deals with chain graphs under the alternative AnderssonMadiganPerlman (AMP) interpretation. In particular, we present a constraint based algorithm for learning an AMP chain graph a given probability distribution is faithful to. We also show that the extension of Meek’s conjecture to AMP chain graphs does not hold, which compromises the development of efficient and correct score+search learning algorithms under assumptions weaker than faithfulness.
Learning Optimal Chain Graphs with Answer Set Programming
"... Learning an optimal chain graph from data is an important hard computational problem. We present a new approach to solve this problem for various objective functions without making any assumption on the probability distribution at hand. Our approach is based on encoding the learning problem declarat ..."
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Cited by 2 (1 self)
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Learning an optimal chain graph from data is an important hard computational problem. We present a new approach to solve this problem for various objective functions without making any assumption on the probability distribution at hand. Our approach is based on encoding the learning problem declaratively using the answer set programming (ASP) paradigm. Empirical results show that our approach provides at least as accurate solutions as the best solutions provided by the existing algorithms, and overall provides better accuracy than any single previous algorithm. 1
Every LWF and AMP Chain Graph Originates From a Set of Causal Models. ArXiv eprints
, 2013
"... ar ..."
LEARNING AMP CHAIN GRAPHS AND SOME MARGINAL MODELS THEREOF UNDER FAITHFULNESS: ADDENDUM
"... A distinguished member of a class of triplex equivalent AMP CGs is the socalled essential graph G ∗ (Andersson and Perlman, 2006): An edge A → B is in G ∗ if and only if A ← B is in no member of the class. Unfortunately, our learning algorithm in Table 1 in the main text does not output an essentia ..."
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Cited by 1 (1 self)
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A distinguished member of a class of triplex equivalent AMP CGs is the socalled essential graph G ∗ (Andersson and Perlman, 2006): An edge A → B is in G ∗ if and only if A ← B is in no member of the class. Unfortunately, our learning algorithm in Table 1 in the main text does not output an essential graph, as we have shown in Section 3 with an example. However, it can easily be modified for this task, as we show below. It is worth mentioning that an algorithm for this task has been proposed before (Andersson and Perlman, 2004, Section 7). However, as far as we know, its correctness has not been proven. We do prove the correctness of our algorithm. Table 1. Algorithm for constructing the essential graph in a class of triplex equivalent CGs. Input: A CG G. Output: The essential graph G ∗ in the class of triplex equivalent CGs containing G. 1 For each ordered pair of nonadjacent nodes A and B in G
Learning Marginal AMP Chain Graphs under Faithfulness
, 2014
"... Marginal AMP chain graphs are a recently introduced family of models that is based on graphs that may have undirected, directed and bidirected edges. They unify and generalize the AMP and the multivariate regression interpretations of chain graphs. In this paper, we present a constraint based algo ..."
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Marginal AMP chain graphs are a recently introduced family of models that is based on graphs that may have undirected, directed and bidirected edges. They unify and generalize the AMP and the multivariate regression interpretations of chain graphs. In this paper, we present a constraint based algorithm for learning a marginal AMP chain graph from a probability distribution which is faithful to it. We also show that the extension of Meek’s conjecture to marginal AMP chain graphs does not hold, which compromises the development of efficient and correct score+search learning algorithms under assumptions weaker than faithfulness.