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## An Inclusion Optimal Algorithm for Chain Graph Structure Learning (2014)

Venue: | In Proceedings of the 17th International Conference on Artificial Intelligence and Statistics |

Citations: | 5 - 5 self |

### Citations

1587 |
Graphical models
- Lauritzen
- 1996
(Show Context)
Citation Context ... G and where k∗ is the smallest k s.t. X,Y ∈ ∪kj=1Cj . If M is a graphoid and G satisfies the local Markov property or the pairwise block-recursive Markov property w.r.t. M , then G is an I map of M (=-=Lauritzen, 1996-=-, Theorem 3.34). We say that a CG Gα is a MI map of an independence model M relative to a chain α if Gα is a MI map of M and Gα is consistent with α. A CG G is said to include an independence model M ... |

248 | Optimal structure identification with greedy search
- Chickering
(Show Context)
Citation Context ...at chain graphs still lack compared to Bayesian networks is an inclusion optimal structure learning algorithm. This has mainly to do with that Meek’s conjecture has been proven for Bayesian networks (=-=Chickering, 2002-=-) but not for chain graphs. We will in this article prove it and, then, use it to Appearing in Proceedings of the 17th International Conference on Artificial Intelligence and Statistics (AISTATS) 2014... |

223 |
Graphical models for associations between variables, some of which are qualitative and some quantitative.
- Lauritzen, Wermuth
- 1989
(Show Context)
Citation Context ...y evaluated. 1 INTRODUCTION This paper deals with chain graphs under the Lauritzen-Wermuth-Frydenberg interpretation. Although these chain graphs were introduced to model independencies fairly early (=-=Lauritzen and Wermuth, 1989-=-), there has been relatively little research on them compared to, for example, Bayesian networks. This has mainly to do with the additional complexity that follows from the fact that chain graphs may ... |

139 | The chain graph Markov property - Frydenberg - 1990 |

93 | Probabilistic Conditional Independence Structures. - Studeny - 2004 |

60 | Linear dependencies represented by chain graphs. - Cox, Wermuth - 1993 |

56 |
Graphical Models: Selecting Causal and Statistical Models, Ph
- Meek
- 1997
(Show Context)
Citation Context ... states that we can transform G into H by a sequence of directed edge additions and covered edge reversals s.t. after each operation in the sequence G is a directed and acyclic graph and I(H) ⊆ I(G) (=-=Meek, 1997-=-). Meek’s conjecture was proven to be true in (Chickering, 2002, Theorem 4) by developing an algorithm that constructs a valid sequence of operations. In this section, we extend Meek’s conjecture from... |

37 | Discrete chain graph models.
- Drton
- 2009
(Show Context)
Citation Context ...compared to Bayesian networks that only have directed edges. Lately, however, chain graphs have got renewed interest due to their ability to represent more independence models than Bayesian networks (=-=Drton, 2009-=-; Ma et al., 2008; Peña, 2009, 2011; Studený, 1997; Studený, 2005; Studený and Bouckaert, 1998; Studený et al., 2009; Volf and Studený, 1999). A key component that chain graphs still lack compar... |

36 | A SINful approach to Gaussian graphical model selection. - Drton, Perlman - 2008 |

28 | On chain graph models for description of conditional independence structures. - Studeny, Bouckaert - 1998 |

26 | On local optima in learning Bayesian networks - Nielsen, Kocka, et al. - 2003 |

17 | On recovery algorithm for chain graphs. - Studeny - 1997 |

10 | Structural Learning of Chain Graphs via Decomposition
- Ma, Xie, et al.
- 2008
(Show Context)
Citation Context ...ayesian networks that only have directed edges. Lately, however, chain graphs have got renewed interest due to their ability to represent more independence models than Bayesian networks (Drton, 2009; =-=Ma et al., 2008-=-; Peña, 2009, 2011; Studený, 1997; Studený, 2005; Studený and Bouckaert, 1998; Studený et al., 2009; Volf and Studený, 1999). A key component that chain graphs still lack compared to Bayesian ne... |

5 | Faithfulness in chain graphs: The discrete case. - Pena - 2009 |

5 | Two operations of merging and splitting components in a chain graph, - Studený, Roverato, et al. - 2009 |

4 | Faithfulness in Chain Graphs: The Gaussian Case - Peña - 2011 |

4 | Learning AMP Chain Graphs under Faithfulness - Peña - 2012 |