An Extension of Lazy Evaluation for Influence Diagrams Avoiding Redundant Variables in the Potentials

Vomlelová, Marta; Jensen, Finn Verner

doi:10.1142/s0218488504002552

Cited by 6 publications

(5 citation statements)

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“…3 However, variable-elimination algorithms developed up to date (Shenoy, 1992;Jensen et al, 1994;Jensen, 2001) were not able to deal with IDs having a structure of super-value nodes such as the one in our example. The algorithms for detecting structural redundancies (Faguiouli and Zaffalon, 1998;Shachter, 1998;Nielsen and Jensen, 1999;Nilsson and Lauritzen, 2000;Vomlelova and Jensen, 2002) have the same shortcoming, so they cannot help the Tatman-Shachter algorithm to remove redundant variables.…”

Section: Related Work and Future Researchmentioning

confidence: 99%

“…All these algorithms try to keep the separability of the utility function as long as possible during the evaluation of the ID, not only for the sake of efficiency, but also to avoid the introduction of redundant variables in the resulting policies. However, all of them may introduce redundant variables, and for this reason some authors have proposed other algorithms that analyze the graph in order to detect those actually required (Faguiouli and Zaffalon, 1998;Shachter, 1998;Nielsen and Jensen, 1999;Nilsson and Lauritzen, 2000;Vomlelova and Jensen, 2002).…”

Section: Introductionmentioning

confidence: 99%

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Variable elimination for influence diagrams with super value nodes

Luque

Díez

2010

International Journal of Approximate Reasoning

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In the original formulation of influence diagrams, each model contained exacly one utility node. Tatman and Shachter (1990) introduced the possibility of having super-value nodes that represent the sum or the product of their parents' utility functions. However the algorithm they proposed for dealing with super-value nodes has two shortcomings: it requires dividing potentials when reversing arcs, and it tends to introduce unnecessary variables in the resulting policies. In this paper we propose a new algorithm for influence diagrams with super-value nodes that avoids these shortcomings and will be in general much more efficient than their arc-reversal algorithm.

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Section: Related Work and Future Researchmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Variable elimination for influence diagrams with super value nodes

Luque

Díez

2010

International Journal of Approximate Reasoning

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“…Finding explanations is a goal pursued within a number of disciplines, such as knowledge-based systems and machine learning. Thus, our approach bears some resemblance to knowledge extraction techniques, such as are used to construct tree-based classifiers [3], oblivious read-once decision graphs [11], rough sets [17], and to identify which nodes are relevant for each decision node in an influence diagram [13,20]. As explained in detail in [7], the KBM2L method tries to reorganize a knowledge structure by a global search for good, representative candidates.…”

Section: Introductionmentioning

confidence: 99%

Explaining clinical decisions by extracting regularity patterns

Bielza

Pozo

Lucas

2008

Decision Support Systems

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When solving clinical decision-making problems with modern graphical decision-theoretic models such as influence diagrams, we obtain decision tables with optimal decision alternatives describing the best course of action for a given patient or group of patients. For real-life clinical problems, these tables are often extremely large. This is an obstacle to understand their content. KBM2L lists are structures that minimize memory storage requirements for these tables, and, at the same time, improve their knowledge organization. The resulting improved knowledge organization can be interpreted as explanations of the decision-table content. In this paper, we explore the use of KBM2L lists in analyzing and explaining optimal treatment selection in patients with non-Hodgkin lymphoma of the stomach using an expert-designed influence diagram as an experimental vehicle. The selection of the appropriate treatment for non-Hodgkin lymphoma of the stomach is, as for many other types of cancer, difficult, mainly because of the uncertainties involved in the decision-making process. In this paper we look at an expert-designed clinical influence diagram as a representation of a body of clinical knowledge. This diagram can be analyzed and explained using KBM2L lists. It is shown that the resulting lists provide high-level explanations of optimal treatments for the disease. These explanations are useful for finding relationships between groups of variables and treatments. It is demonstrated that these lists can act as a basis for gaining a deeper understanding of the underlying clinical problem.

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“…The problem of redundant variables is not specific for UIDs, but also occurs when solving e.g. influence diagrams using standard solution algorithms (see alsoVomlelova and Jensen (2004)). …”

mentioning

confidence: 99%

A comparison of two approaches for solving unconstrained influence diagrams

Ahlmann-Ohlsen¹,

Jensen²,

Nielsen³

et al. 2009

International Journal of Approximate Reasoning

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Influence diagrams and decision trees represent the two most common frameworks for specifying and solving decision problems. As modeling languages, both of these frameworks require that the decision analyst specifies all possible sequences of observations and decisions (in influence diagrams, this requirement corresponds to the constraint that the decisions should be temporarily linearly ordered). Recently the unconstrained influence diagram was proposed to address this drawback. In this framework, we may have a partial ordering of the decisions, and a solution to the decision problem therefore consists not only of a decision policy for the various decisions, but also of a conditional specification of what to do next. Relative to the complexity of solving an influence diagram, finding a solution to an unconstrained influence diagram may be computationally very demanding w.r.t. both time and space. Hence, there is a need for efficient algorithms that can deal with (and take advantage of) the idiosyncrasies of the language. In this paper we propose two such solution algorithms. One resembles the variable elimination technique from influence diagrams, whereas the other is based on conditioning and supports any-space inference. Finally we present an empirical comparison of the proposed methods.

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An Extension of Lazy Evaluation for Influence Diagrams Avoiding Redundant Variables in the Potentials

Cited by 6 publications

References 5 publications

Variable elimination for influence diagrams with super value nodes

Variable elimination for influence diagrams with super value nodes

Explaining clinical decisions by extracting regularity patterns

A comparison of two approaches for solving unconstrained influence diagrams

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