Madigan, D., Mosurski, K., and Almond, R. 1996. Explanation in Belief Networks. J. Comp. and Graphical Stat. 6:160--181.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....variable of interest. Weights of evidence combine additively and provide a simple foundation for graphical explanations of numerical results. Other approaches concentrated on verbal (e.g. 8, 16, 19] or graphical (e.g. 3] methods for explaining single step Bayesian updating. Madigan et al. [15] proposed a collection of graphical methods for explaining inference in graphical models. Of verbal explanations, two types addressed large models (as opposed to local interactions) scenario based approach [4, 11] and belief propagation based approach [11, 21] In this paper, we concentrate on ....

David Madigan, Krzysztof Mosurski, and Russell G. Almond. Explanation in belief networks. (under review), 1994.

.... effective see, for example, Bauer and Kohavi [1998] Elkan s application of boosted na ve Bayes won first place out of 45 entries in the data mining competition KDD 97 (Elkan [1997] However, while the regular na ve Bayes approach leads to elegant and effective explanations (see, for example, Madigan, et al. [1996] and Becker, et al. [1997] the AdaBoost ed version destroys this feature. Boosting and Weights of Evidence Under the na ve Bayes assumption, writing the log odds in favor of Y=1 we obtain the following: # # # # # # # # # # # # # # d j j d j j j X w w Y X P Y X P Y P Y P X Y P X Y P 1 0 1 ) ....

....in favor of the hypothesis that Y=1. A negative weight is evidence for Y=0. Spiegelhalter and KnillJones [1984] advocate the use of weights of evidence extensively in medical diagnosis and propose evidence balance sheets as a means of viewing the reasoning process of the na ve Bayes classifier. Madigan, et al. [1996] and Becker, et al. [1997] develop this idea further. In what follows, we derive a boosted weight of evidence that the explanation facilities of Madigan, et al. [1996] and Becker, et al. [1997] can use directly. Writing the AdaBoost combined classifiers, H(x) in the form of a log odds simplifies ....

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Madigan, David, K. Mosurski, and R.G. Almond [1996] Explanation in Belief Networks. Journal of Computational and Graphical Statistics, 6, 160-181.

....for HUGIN propagation. 6 An application: Sensitivity analysis Sensitivity analysis is part of explanation, which has to do with explaining to a user how the system has arrived at its conclusions. Explanation for Bayesian networks has been studied systematically by Suermondt (1992) and Madigan Mosurski (1993) have implemented various explanation facilities. Some of the questions to answer in connection to explanation concern the sensitivity of the conclusions to the particular evidence. Let h be a hypothesis (in the form of a particular configuration of states for some hypothesis variables) and let e ....

Madigan, D. & Mosurski, K. (1993). Explanation in belief networks, Technical report, University of Washington, US and Trinity College, Dublin, Ireland.

....many hybrids. ffl They come with well understood techniques for key tasks in the discovery process: problem formulation and decomposition, designing a learning algorithm (Buntine 1994) identification of valuable knowledge (using decision theory) and generation of explanations (Madigan, Mosurski, and Almond 1995). Only a simple form of graphical model is considered in this chapter, the Bayesian network. Reasoning about the value of knowledge on Bayesian networks can be done by adding value nodes, and using the tools of influence diagrams and utility theory (Shachter 1986) part of modern decision ....

Madigan, D., Mosurski, K., and Almond, R.G. 1995. Explanation in belief networks.

....Milwaukee WI 53201 Tel: 414 229 4955 Fax: 414 229 6958 y Section of Information and Decision Sciences Department of Radiology Medical College of Wisconsin Milwaukee, WI 53226 Tel: 414 259 2173 Fax: 414 259 9290 z Introl Corp. 301 N. Water Street Milwaukee, WI 53202 Tel: 273 6100 September 15, 1996 To appear in Artificial Intelligence in Medicine. Abstract We present an educational tool for bringing the information contained in a Bayesian network to the end user in an easily intelligible form. The banter shell is designed to tutor users in evaluation of hypotheses and selection of ....

....is generated as a list of elementary qualitative inferences, along with any summary conclusions. In later work, Druzdzel and Henrion [ 8 ] extend their method for qualitative propagation in QPNs to general multiply connected networks and present a polynomial time algorithm. Madigan, etal [ 14 ] describe an approach to explanation in belief networks based on visualizing the propagation of evidence through the network. The described techniques have been implemented in a system called graphical belief, which is a belief network modeling package [ 2 ] They use Good s weight of evidence [ ....

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D. Madigan, K. Mosurski, and R.G. Almond. Explanations in belief networks. Journal of Computational and Graphical Statistics, 1996. To appear.

....discuss the power of graphic representations of knowledge in ITS s. In fact, it may be an advantage to make the graph available to the student during instruction and graphically explain the student s progress through the domain. Explanation facilities for graphical models have been developed by Madigan et al. 1994) and Suermondt (1992) 3 Teaching Operators A teaching operator is a self contained, instructional module, designed to teach one or more expert facets, and or remediate one or more inexpert facets (the tutoring primitives of Woolf (1992) are defined similarly) Typically, for the majority of ....

Madigan, D., Mosurski, K., and Almond, R. (1994). Explanation in Belief Networks. Under revision at the Journal of Computational Graphics and Statistics.

....in the associated undirected graph (see Dawid, 1992) contain no more than one node. David Madigan and Russell G. Almond 9.3. 1 Weight of evidence in Berge Networks and Markov Trees In a Berge network, the expected weight of evidence decreases in a monotone fashion away from the hypothesis, H (Madigan et al. 1994). Therefore, for these networks, the test selection strategy can confine its attention to the immediate neighbors of H. This convenient property derives from the following basic result: Theorem 1 (Monotonicity) In a belief network with three nodes (A, B and H) if B separates A from H (Figure ....

....no more than the weight of evidence B provides for H. Berge networks have the property that for any pair of connected nodes, the network is collapsible onto a unique evidence chain connecting the two nodes. A simple recursion argument extends the above monotonicity property to these chains see Madigan et al. 1994) for details. For non Berge networks, no similar property exists. Consider the example of Figure 2. Although EW (H : B;C) EW (H : A) it could be true that EW (H : A) EW (H : B) and EW (H : A) EW (H : C) Simply searching all of the neighbors of the target hypothesis is not sufficient for ....

Madigan, D., Mosurski, K., and Almond, R.G. [1994]. "Explanation in Belief Networks." Submitted for publication.

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Madigan, D., Mosurski, K., and Almond, R. 1996. Explanation in Belief Networks. J. Comp. and Graphical Stat. 6:160--181.

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Madigan, D., Mosurski, K. and Almond R.G., Explanation in belief networks. Technical Report, Department of Statistics, University of Washington, 1994.

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Madigan, D., Mosurski, K. and Almond R.G., Explanation in belief networks. Technical Report, Department of Statistics, University of Washington, 1994.

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