## Graphical Explanation in Belief Networks (1997)

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Venue: | In Journal of Computational and Graphical Statistics |

Citations: | 18 - 5 self |

### BibTeX

@ARTICLE{Madigan97graphicalexplanation,

author = {David Madigan and Krzysztof Mosurski and Russell G Almond},

title = {Graphical Explanation in Belief Networks},

journal = {In Journal of Computational and Graphical Statistics},

year = {1997},

volume = {6},

pages = {160--181}

}

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### Abstract

Belief networks provide an important bridge between statistical modeling and expert systems. In this paper we present methods for visualizing probabilistic "evidence flows" in belief networks, thereby enabling belief networks to explain their behavior. Building on earlier research on explanation in expert systems, we present a hierarchy of explanations, ranging from simple colorings to detailed displays. Our approach complements parallel work on textual explanations in belief networks. GRAPHICAL-BELIEF, Mathsoft Inc.'s belief network software, implements the methods. 1 Introduction A fundamental reason for building a mathematical or statistical model is to foster deeper understanding of complex, real-world systems. Consequently, explanations---descriptions of the mechanisms which comprise such models---form an important part of model validation, exploration, and use. Early tests of rule-based expert system models indicated the critical need for detailed explanations in that setting (...

### Citations

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(Show Context)
Citation Context ...tatistics Box 354322, University of Washington, Seattle WA 981954322. E-mail: madigan@stat.washington.edu. WWW: http://bayes.stat.washington.edu. 2 Belief networks (Lauritzen and Spiegelhalter, 1988; =-=Pearl, 1988-=-; Almond, 1995a, Spiegelhalter, et al., 1993) provide an important bridge between statistical modeling and expert system modeling. Formally, a belief network is a set of probability measures defined b... |

1343 |
Local Computations with Probabilities on Graphical Structures and their Application to Expert Systems
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(Show Context)
Citation Context ...for correspondence: Department of Statistics Box 354322, University of Washington, Seattle WA 981954322. E-mail: madigan@stat.washington.edu. WWW: http://bayes.stat.washington.edu. 2 Belief networks (=-=Lauritzen and Spiegelhalter, 1988-=-; Pearl, 1988; Almond, 1995a, Spiegelhalter, et al., 1993) provide an important bridge between statistical modeling and expert system modeling. Formally, a belief network is a set of probability measu... |

524 |
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Citation Context ...e flows in this example. Fortunately, there does exist a class of belief networks that is more general than trees and facilitates the graphical explanations introduced in Section 3.2. Berge networks (=-=Berge, 1976-=-) are chordal graphs with clique intersections of size one (an undirected graph is chordal if all cycles of length greater than three in the graph have a connection between two intermediate nodes of t... |

321 | Rule-based Expert System: The MYCIN Experiments of the Stanford Heuristic Programming Projects - Buchanan, Shortli - 1984 |

292 | Model Selection and Accounting for Model Uncertainty in Graphical Models Using Occam’s Window
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Citation Context ...ntly desirable to consider several belief network models simultaneously. These models may be provided by a number of experts or may arise from a model selection procedure (Edwards and Havranek, 1985, =-=Madigan and Raftery, 1994-=-). Explanations could be averaged over the different models under consideration. Ideally, these would be integrated with support for making comparisons between models, such as proposed in Almond (1994... |

229 | Scientific Explanation and the Causal Structure of the World - Salmon - 1984 |

204 |
Brushing Scatterplots
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Citation Context ...el in which the explanation is dynamically generated in response to user queries. This should have similar strengths to other analysis methods built on dynamic graphics, such as scatterplot brushing (=-=Becker and Chambers, 1987-=-). We have implemented the methods of this paper in GRAPHICAL-BELIEF, Mathsoft, Inc.'s belief network modeling software (Almond, 1995b). All the color figures are taken directly from that software. Wh... |

197 |
Bayesian analysis in expert systems
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Citation Context ...sity of Washington, Seattle WA 981954322. E-mail: madigan@stat.washington.edu. WWW: http://bayes.stat.washington.edu. 2 Belief networks (Lauritzen and Spiegelhalter, 1988; Pearl, 1988; Almond, 1995a, =-=Spiegelhalter, et al., 1993-=-) provide an important bridge between statistical modeling and expert system modeling. Formally, a belief network is a set of probability measures defined by distributional assumptions (such as multiv... |

153 | Bayesian updating in recursive graphical models by local computation - Jensen, Lauritzen, et al. - 1990 |

144 | Independence properties of directed Markov fields - Lauritzen, Dawid, et al. - 1990 |

139 | Axioms for probability and belief-function propagation - Shenoy, Shafer - 1990 |

138 |
Petri Nets
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Citation Context ...eight of evidence for X 1 (as indicated by the width of the outer bar on the rightmost link) and will block incoming evidence. 15 As an alternative to Figure 9, we can use the idea of "Petri toke=-=ns" (Reisig, 1985-=-) to dynamically show the flow of evidence along the chain. Figure 10 shows such an evidence flow. The width of the balls encodes the actual weight of evidence and the width of the channel encodes the... |

103 | XPLAIN: A System for Creating and Explaining Expert Consulting Programs, USC/Information Sciences Institute - Swartout - 1982 |

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Citation Context ...on of the independencies. The graph serves as both a visual representation of the model (a sort of informal explanation) and a guide to efficient probability computation algorithms (see, for example, =-=Dawid, 1992). In what-=- follows, we will refer to the graph as the "belief network". In recent years, researchers in Statistics and in Computer Science have directed considerable attention at belief networks for d... |

60 | An approximate nonmyopic computation for value of information - Heckerman, Horvitz, et al. - 1993 |

54 |
Graphical belief modeling
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Citation Context ... 354322, University of Washington, Seattle WA 981954322. E-mail: madigan@stat.washington.edu. WWW: http://bayes.stat.washington.edu. 2 Belief networks (Lauritzen and Spiegelhalter, 1988; Pearl, 1988; =-=Almond, 1995-=-a, Spiegelhalter, et al., 1993) provide an important bridge between statistical modeling and expert system modeling. Formally, a belief network is a set of probability measures defined by distribution... |

49 |
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Citation Context ... suggested that it is frequently desirable to consider several belief network models simultaneously. These models may be provided by a number of experts or may arise from a model selection procedure (=-=Edwards and Havranek, 1985-=-, Madigan and Raftery, 1994). Explanations could be averaged over the different models under consideration. Ideally, these would be integrated with support for making comparisons between models, such ... |

43 | Qualitative Propagation and Scenario-based Approaches to Explanation - Henrion, Druzdzel - 1991 |

40 | Distributed revision of composite beliefs - Pearl - 1987 |

39 | Probabilistic reasoning in predictive expert systems - Spiegelhalter - 1986 |

37 | A causal calculus (i - Good - 1961 |

28 |
Explaining Control Strategies in Problem Solving
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Citation Context ..., and use. Early tests of rule-based expert system models indicated the critical need for detailed explanations in that setting (Buchanan and Shortliffe, 1984; Barr and Feigenbaum, 1982; Coyne, 1990; =-=Chandrasakaran, et al., 1989). Us-=-ers of these early systems found that understanding why the system had reached a particular conclusion or decision was as important as reaching the decision. Swartout (1983) comments that "trust ... |

28 | Weight of evidence: a brief survey - Good - 1985 |

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9 |
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Citation Context ..., exploration, and use. Early tests of rule-based expert system models indicated the critical need for detailed explanations in that setting (Buchanan and Shortliffe, 1984; Barr and Feigenbaum, 1982; =-=Coyne, 1990-=-; Chandrasakaran, et al., 1989). Users of these early systems found that understanding why the system had reached a particular conclusion or decision was as important as reaching the decision. Swartou... |

7 | Statistical Principles on Graphs - Smith - 1990 |

6 |
Explicativity: a mathematical theory of explanation with statistical applications
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(Show Context)
Citation Context ...ef network. This paper describes an approach to explanation in belief networks based primarily on visualizing the propagation of evidence through the belief network. We use Good's weight of evidence (=-=Good, 1977) as our b-=-asic metric of explanatory power and the graph itself to provide context for the "evidence flows". We envision these explanations as part of a graphical display of the model in which the exp... |

5 |
An extension of the results of Asmussen and Edwards on collapsibility in contingency tables
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(Show Context)
Citation Context ...3 is collapsible onto (S,D), since the induced subgraph on (S,D) contains an edge and does not imply any new independencies. For a given chordal graph, G, and a set of nodes, SsV, the SAHR algorithm (=-=Madigan and Mosurski, 1990-=-) finds SsV, the (unique) smallest set of nodes containing S such that the model 17 defined by G is collapsible onto S. The SAHR algorithm recursively removes simplicial vertices from G\S (a node v e ... |

4 | Explanation of probabilistic inference in Bayesian belief networks - Suermondt - 1991 |

3 |
D.,A.,"Probability and the Processes of Discovery, Proof, and Choice
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Citation Context ...ch as an observation or a test result), for a target hypothesis, H (such as a disease state). Let H be the hypothesis and H its negation. The weight of evidence (Good, 1977, 1985, van Fraassen, 1980, =-=Schum, 1988-=-) for H provided by E is: W(H:E) = log Pr(E|H) Pr(E|H) Good (1985) provides a comprehensive review of the properties of weights of evidence and presents a detailed justification for using weights of e... |

3 | Coherent evidence propagation in expert systems - Spiegelhalter - 1987 |

2 | Statistical and knowledge based approaches to clinical decision support systems, with an application in gastroenterology (with discussion - Spiegelhalter, Knill-Jones - 1984 |

1 |
GRAPHICAL-BELIEF Overview. World Wide Web: http://bayes.stat.washington.edu/almond/gb/graphical-belief.html
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Citation Context ... 354322, University of Washington, Seattle WA 981954322. E-mail: madigan@stat.washington.edu. WWW: http://bayes.stat.washington.edu. 2 Belief networks (Lauritzen and Spiegelhalter, 1988; Pearl, 1988; =-=Almond, 1995-=-a, Spiegelhalter, et al., 1993) provide an important bridge between statistical modeling and expert system modeling. Formally, a belief network is a set of probability measures defined by distribution... |

1 | Brushing Histories to Compare Models. StatSci Research Report 17 - Almond - 1994 |

1 | Explanation in causal networks - Chamberlain, Nordahl - 1988 |

1 | Knowledge Based Systems : The User Interface - Cleal, Heaton - 1988 |

1 |
Significant factors in ultrasound-imaged piezo-electric extracorporeal shockwave lithotripsy
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Citation Context ...culus with inability to find it at the time of operation. In recent years, Extracorporeal Shock Wave Lithotripsy (ESWL) has become established as the most popular treatment for urinary tract calculi (=-=Kiely, et al., 1989-=-, Lingeman, et al., 1987, Marberger, et al., 1988). ESWL focuses 4 hundreds of high frequency shockwaves on the stone, creating high energy at the point of focus. This disintegrates the stone, which i... |

1 |
Management of upper ureteral calculi with extracorporeal shockwave lithotripsy
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(Show Context)
Citation Context ...to find it at the time of operation. In recent years, Extracorporeal Shock Wave Lithotripsy (ESWL) has become established as the most popular treatment for urinary tract calculi (Kiely, et al., 1989, =-=Lingeman, et al., 1987-=-, Marberger, et al., 1988). ESWL focuses 4 hundreds of high frequency shockwaves on the stone, creating high energy at the point of focus. This disintegrates the stone, which is then cleared by the no... |

1 | An investigation of weights of evidence in the context of probabilistic expert systems - Madigan - 1989 |

1 | On test selection measures for belief networks - Madigan, Almond - 1995 |

1 |
Painless piezoelectric extracorporeal lithotripsy
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Citation Context ...f operation. In recent years, Extracorporeal Shock Wave Lithotripsy (ESWL) has become established as the most popular treatment for urinary tract calculi (Kiely, et al., 1989, Lingeman, et al., 1987, =-=Marberger, et al., 1988-=-). ESWL focuses 4 hundreds of high frequency shockwaves on the stone, creating high energy at the point of focus. This disintegrates the stone, which is then cleared by the normal functioning of the k... |

1 |
Giant ureteral calculus
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Citation Context ... males than in females, seldom occur in black skinned people and are particularly common in certain geographical regions with a dry hot climate. Calculi have been found weighing as much as 286 grams (=-=Mayers, 1940-=-). Historically, stones have been treated by inducing the spontaneous passage of the stone with various drugs and failing that, operative removal. There are many dangers associated with the operative ... |

1 | Information theoretic measures of fit for univariate and multivariate linear regressions - Theil, Chang - 1988 |