## Tractable Structure Search in the Presence of Latent Variables

Citations: | 1 - 1 self |

### BibTeX

@MISC{Richardson_tractablestructure,

author = {Thomas Richardson and Heiko Bailer and Moulinath Banerjee},

title = {Tractable Structure Search in the Presence of Latent Variables},

year = {}

}

### OpenURL

### Abstract

The problem of learning the structure of a DAGmodel in the presence of latent variables presents many formidable challenges. In particular there are an infinite number of latent variable models to consider, and these models possess features which make them hard to work with. We describe a class of graphical models which can represent the conditional independence structure induced by a latent variable model over the observed margin. We give a parametrization of the set of Gaussian distributions with conditional independence structure given by a MAG model. The models are illustrated via a simple example. Different estimation techniques are discussed in the context of Zellner's Seemingly Unrelated Regression (SUR) models. Keywords: Multivariate Graphical Models; Causal Modelling; Latent Variables; Ancestral Graphs; MAG Models. 1 INTRODUCTION There has been significant progress in the development of algorithms for learning the directed acyclic graph (DAG) part of a Bayes...

### Citations

7414 | Probabilistic reasoning in intelligent systems: Networks of plausible inference - Pearl - 1988 |

1127 | A Bayesian method for the induction of probabilistic networks from data. Machine Learning 9:309–347
- Cooper, Herskovits
- 1992
(Show Context)
Citation Context ...ION There has been significant progress in the development of algorithms for learning the directed acyclic graph (DAG) part of a Bayesian network from complete data and optional background knowledge (=-=Cooper and Herskovits, 1992-=-; Spirtes, Glymour and Scheines, 1993; Heckerman, Geiger and Chickering, 1994). However, the problem of learning the DAG part of a Bayesian network with latent (unmeasured) variables is more difficult... |

461 | Graphical Models in Applied Multivariate Statistics - Whittaker - 1990 |

223 |
Equivalence and synthesis of causal models
- Verma, Pearl
- 1990
(Show Context)
Citation Context ...MARKOV EQUIVALENCE The existence of equivalent, yet structurally distinct, DAG models is a central problem when attempting to identify cause-effect relationships (Spirtes, Glymour and Scheines, 1993; =-=Verma and Pearl, 1990-=-). It is important to identify statistically equivalent structures, since they may have different causal interpretations. Data fitting a model M well can be regarded as evidence for some feature of th... |

213 | A theory of inferred causation - Pearl, Verma - 1991 |

201 | Covariance selection - Dempster - 1972 |

133 | Learning equivalence classes of Bayesian network structures
- Chickering
- 1996
(Show Context)
Citation Context ...ficient to score many different structures if it is inevitable that they will all receive the same score. In the case of DAG models without latent variables a number of authors (Madigan et al., 1996; =-=Chickering, 1995-=-; Spirtes and Meek, 1995) have performed model searches which consider equivalence classes of models. Figure 5 shows three MAGs that are Markov equivalent (hence statistically equivalent) to the MAG i... |

79 |
The methods of path coefficients
- Wright
- 1934
(Show Context)
Citation Context ...ced by Zellner (1962). SUR models and associated estimation techniques are discussed in sections 8 & 9. Sewall Wright's path diagrams also contain double headed arrows representing correlated errors (=-=Wright, 1934-=-). 5 EXAMPLE: COCHRAN'S NOCTUID MOTH DATA To illustrate the use of MAG models we consider the data on moth trappings, which originally appeared in the statistical literature in a paper of Cochran (193... |

77 | Learning bayesian networks: Search methods and experimental results - Chickering, Geiger, et al. - 1995 |

57 | Learning Bayesian networks with discrete variables from data
- Spirtes, Meek
- 1995
(Show Context)
Citation Context ...any different structures if it is inevitable that they will all receive the same score. In the case of DAG models without latent variables a number of authors (Madigan et al., 1996; Chickering, 1995; =-=Spirtes and Meek, 1995-=-) have performed model searches which consider equivalence classes of models. Figure 5 shows three MAGs that are Markov equivalent (hence statistically equivalent) to the MAG in Figure 4(c). In fact i... |

40 | Multivariate Dependencies - Cox, Wermuth - 1996 |

22 | Graphical models and exponential families - Geiger, Meek - 1998 |

21 | The omission or addition of an independent variate in multiple linear regression - Cochran - 1938 |

15 | A Polynomial Time Algorithm For Determining DAG Equivalence - Spirtes, Richardson - 1996 |

5 | An Experiment in Causal Discovery Using a Pneumonia Database - Spirtes, Cooper - 1997 |