## Modeling Discrete Interventional Data using Directed Cyclic Graphical Models

Citations: | 8 - 0 self |

### BibTeX

@MISC{Schmidt_modelingdiscrete,

author = {Mark Schmidt and Kevin Murphy},

title = {Modeling Discrete Interventional Data using Directed Cyclic Graphical Models},

year = {}

}

### OpenURL

### Abstract

We outline a representation for discrete multivariate distributions in terms of interventional potential functions that are globally normalized. This representation can be used to model the effects of interventions, and the independence properties encoded in this model can be represented as a directed graph that allows cycles. In addition to discussing inference and sampling with this representation, we give an exponential family parametrization that allows parameter estimation to be stated as a convex optimization problem; we also give a convex relaxation of the task of simultaneous parameter and structure learning using group ℓ1regularization. The model is evaluated on simulated data and intracellular flow cytometry data. 1

### Citations

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Citation Context ...aluated on simulated data and intracellular flow cytometry data. 1 Introduction Graphical models provide a convenient framework for representing independence properties of multivariate distributions (=-=Lauritzen, 1996-=-). There has been substantial recent interest in using graphical models to model data with interventions, that is, data where some of the variables are set experimentally. Directed acyclic graphical (... |

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Citation Context ...s closely related to a variety of previous methods that express joint distributions in terms of conditional distributions. For example, the classic work on pseudo-likelihood for parameter estimation (=-=Besag, 1975-=-) considers optimizing the set of conditional distributions as a surrogate to optimizing thejoint distribution. Heckerman et al. (2000) have advocated the advantages of dependency networks, directed ... |

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Citation Context ...nt distribution defined by their product, nor has it considered modeling the effects of interventions. Our work is also closely related to work on path diagrams and structural equation models (SEMs) (=-=Wright, 1921-=-), models of functional dependence that have long been used in genetics, econometrics, and the social sciences (see Pearl (2000)). Spirtes (1995) discusses various aspects of ‘non-recursive’ SEMs, whi... |

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Citation Context ...a particular edge e is equivalent to removing the edge from the graph. This type of approach to simultaneous parameter and structure learning has previously been e explored for undirected graphs (see =-=Lee et al., 2006-=-; Schmidt et al., 2008), but can not be used directly for DAG models (unless we restrict ourselves to a fixed node ordering) because of the acyclicity constraint. Similar to Schmidt et al. (2008), we ... |

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Citation Context ...e is equivalent to removing the edge from the graph. This type of approach to simultaneous parameter and structure learning has previously been e explored for undirected graphs (see Lee et al., 2006; =-=Schmidt et al., 2008-=-), but can not be used directly for DAG models (unless we restrict ourselves to a fixed node ordering) because of the acyclicity constraint. Similar to Schmidt et al. (2008), we can convert the contin... |

38 |
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Citation Context ...r SEMs. Pearl and Dechter (1996) prove an analogous result that d-separation is valid for feedback systems involving discrete variables. Modeling the effects of interventions in SEMs is discussed in (=-=Strotz and Wold, 1960-=-). Richardson (1996a,b) examines the problem of deciding Markov equivalence of directed cyclic graphical models, and proposes a method to find the structure of directed cyclic graphs. Lacerda et al. (... |

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1 | Variations on undirected graphical models and their relationships - Heckerman, Meek, et al. |