## Explanation Trees for Causal Bayesian Networks

Citations: | 3 - 0 self |

### BibTeX

@MISC{Nielsen_explanationtrees,

author = {Ulf H. Nielsen and André Elissee},

title = {Explanation Trees for Causal Bayesian Networks},

year = {}

}

### OpenURL

### Abstract

Bayesian networks can be used to extract explanations about the observed state of a subset of variables. In this paper, we explicate the desiderata of an explanation and confront them with the concept of explanation proposed by existing methods. The necessity of taking into account causal approaches when a causal graph is available is discussed. We then introduce causal explanation trees, based on the construction of explanation trees using the measure of causal information ow (Ay and Polani, 2006). This approach is compared to several other methods on known networks. 1

### Citations

7487 |
Probabilistic Reasoning in Intelligent Systems: Networks of Plausible Inference
- Pearl
- 1988
(Show Context)
Citation Context ...ion of explanation trees using the measure of causal information ow (Ay and Polani, 2006). This approach is compared to several other methods on known networks. 1 INTRODUCTION A Bayesian network (BN, =-=Pearl, 1988-=-) is an algebraic tool to compactly represent the joint probability distribution of a set of variables V by exploiting conditional independence amongst variables. It represents all variables in a dire... |

1348 |
Local computations with probabilities on graphical structures and their application to expert systems (with discussion
- Lauritzen, Spiegelhalter
- 1988
(Show Context)
Citation Context ...seem intuitively likely. BF provides more concise explanations, but, like ET, ignores Practice altogether, although a bad practice can account for failure equally well. Asia (Figure 5). This network (=-=Lauritzen and Spiegelhalter, 1988-=-) models the relationships between two indicators, X-ray results and dyspnea, of severe diseases for a person. Tuberculosis (more likely if a visit to Asia occurred) and lung cancer (more likely when ... |

1285 | Factor graphs and the sum-product algorithm
- Kschischang, Frey, et al.
- 2001
(Show Context)
Citation Context ...ns by using the graphical reachability criterion from a candidate node X to E, blocking paths going through O∪P. The inference steps were implemented using the factor graph message-passing algorithm (=-=Frey et al., 2001-=-). The complexity of this algorithm, in terms of number of calls to an inference engine per node in the constructed tree, is O(nd), where n is the number of explanatory variables |H| and d is the aver... |

1267 |
Causality: models, reasoning and inference
- Pearl
- 2000
(Show Context)
Citation Context ...ly representing the structure of the dependencies between the variables, BNs allow inference tasks to be solved more e ciently. In this paper, we discuss the extraction of explanations in causal BNs (=-=Pearl, 2000-=-; Spirtes et al., 2001) BNs where the arcs depict direct cause e ect relationships between variables. Generally, explanations in BNs can be classi ed in three categories (Lacave and Diez, 2002) depend... |

570 |
Theory of Probability
- Jeffreys
- 1961
(Show Context)
Citation Context ...d is best described with the example of Simpson’s paradox in Pearl (2000), chap. 6. SE analysis also works by comparing two explanations hi and hj, usually with Bayes’ factor or the likelihood ratio (=-=Jeffreys, 1961-=-): Bayes’ factor = posterior ratio prior ratio = p(hi | e) / p(hj | e) p(e | hi) = p(hi) / p(hj) p(e | hj) . The empirical interpretation of Bayes’ factor given by Jeffreys (1961) is that if it is les... |

187 | Causal diagrams for empirical research - Pearl - 1995 |

134 | Causes and explanations: A structural-model approach. part I: Causes - Halpern, Pearl - 2005 |

38 | MAP complexity results and approximation methods
- Park
- 1991
(Show Context)
Citation Context ...rivial issue (Shimony, 1991).Partial abduction is computationally more expensive than standard MPE, because it cannot be readily solved by message passing algorithms, but approximations exist (e.g., =-=Park, 2002-=-). On the other hand, it globally leads to more concise explanations than MPE. Further e orts to make explanations more concise include de Campos et al. (2001), where the k most probable explanations ... |

29 | A review of explanation methods for Bayesian networks - Lacave, Diez |

23 | Defining explanation in probabilistic systems
- Chajewska, Halpern
- 1997
(Show Context)
Citation Context ... o for variables both in H and in O). explanatory variables H all variables V explanandum E = e observed variables O = o We insist on the distinction between the explanandum e and the observations o (=-=Chajewska and Halpern, 1997-=-). Observations are all our knowledge about the current state of a system, and this might not coincide exactly with what we want explained. Consider for example the case where we wish to know why the ... |

22 |
Information flows in causal networks
- Ay, Polani
(Show Context)
Citation Context ...usal approaches when a causal graph is available is discussed. We then introduce causal explanation trees, based on the construction of explanation trees using the measure of causal information flow (=-=Ay and Polani, 2006-=-). This approach is compared to several other methods on known networks. 1 INTRODUCTION A Bayesian network (BN, Pearl, 1988) is an algebraic tool to compactly represent the joint probability distribut... |

17 |
Explanation, irrelevance and statistical independence
- Shimony
- 1991
(Show Context)
Citation Context ...cause of lack of conciseness; moreover, it is hard to distinguish between long explanations, whose respective probabilities are low anyway and close to one another. In the partial abduction approach (=-=Shimony, 1991-=-), the set of explanatory variables is a strict subset H � V \ E. The set of variables X = V \ H \ E excluded from the explanation is then marginalized out before ∑ the maximum is computed: we look fo... |

15 | Theory of Probability - reys, H - 1948 |

11 | Qualitative propagation and scenario-based schemes for explaining probabilistic reasoning - Henrion, Druzdzel - 1991 |

5 | On the robustness of most probable explanations
- Chan, Darwiche
- 2006
(Show Context)
Citation Context ...explanations, are not robust: little changes in the network will often change the result of the analysis, even though the changes occur in parts of the network largely independent of the explanandum (=-=Chan and Darwiche, 2006-=-). Common to the methods in this subsection is that they order explanations by p(h, e) (this is equivalent to p(h | e) as p(e) is constant for a given e): this joint probability cannot be considered a... |

3 |
De ning explanation in probabilistic systems
- Chajewska, Halpern
- 1997
(Show Context)
Citation Context ... o for variables both in H and in O). explanatory variables H all variables V explanandum E = e observed variables O = o We insist on the distinction between the explanandum e and the observations o (=-=Chajewska and Halpern, 1997-=-). Observations are all our knowledge about the current state of a system, and this might not coincide exactly with what we want explained. Consider for example the case where we wish to know why the ... |

2 |
N.: Information ows in causal networks
- Polani, Ay
- 2007
(Show Context)
Citation Context ...causal approaches when a causal graph is available is discussed. We then introduce causal explanation trees, based on the construction of explanation trees using the measure of causal information ow (=-=Ay and Polani, 2006-=-). This approach is compared to several other methods on known networks. 1 INTRODUCTION A Bayesian network (BN, Pearl, 1988) is an algebraic tool to compactly represent the joint probability distribut... |

2 | Simplifying explanations in Bayesian belief networks - Campos, Gémez, et al. - 2001 |

2 | Bayesian networks inference: Advanced algorithms for triangulation and partial abduction - Flores - 2005 |

1 | On causal explanations in Bayesian networks - Nielsen - 2007 |