Structuring Conditional Relationships in Influence Diagrams

Abstract

An influence diagram is a graphical representation of a decision problem that is at once a formal description of a decision problem that can be treated by computers and a representation that is easily understood by decision makers who may be unskilled in the art of complex probabilistic modeling. The power of an influence diagram, both as an analysis tool and a communication tool, lies in its ability to concisely summarize the structure of a decision problem. However, when confronted with highly asymmetric problems in which particular acts or events lead to very different possibilities, many analysts prefer decision trees to influence diagrams. In this paper, we extend the definition of an influence diagram by introducing a new representation for its conditional probability distributions. This extended influence diagram representation, combining elements of the decision tree and influence diagram representations, allows one to clearly and efficiently represent asymmetric decision problems and provides an attractive alternative to both the decision tree and conventional influence diagram representations.

The Usage of Influence Diagram for Decision Making in Textiles

“…The problem is presented in three levels which are relational, functional and numerical (Smith et al 1993). It is a fact that when a decision tree have too many decision alternatives and chance variables, it turns into a very complex structure.…”

Sequential valuation networks for asymmetric decision problems

“…Representing this problem using Smith-Holtzman-Matheson's [1993] asymmetric influence diagrams or Shenoy's [2000] asymmetric valuation networks is possible but only after either introducing additional variables or introducing dummy states for the existing variables. This is because if one uses the existing variables, the modeling of information constraints would depend on the FT decision.…”

“…Several graphical techniques have been proposed for representing and solving asymmetric decision problems-traditional decision trees, Call and Miller's [1990] combination of influence diagrams (IDs) and decision trees, Fung and Shachter's [1990] contingent IDs, Smith, Holtzman and Matheson's [1993] IDs with distribution trees, and Qi et al's [1994] decision graphs within the ID framework, Shenoy's [2000] asymmetric valuation network representation with indicator valuations, Covaliu and Oliver's [1995] sequential decision diagrams, Liu and Shenoy's [1995] configuration networks, Nielsen and Jensen's [2000] asymmetric IDs, and Liu and Shenoy's [2004] VNs with coarse valuations. Each of these methods has some advantages and disadvantages.…”

Data mining with graphical models

“…Particularly for Bayesian networks several approaches to exploit such regularities have been studied in order to capture additional (i.e., context specific) independences and, as a consequence, to (potentially) enhance evidence propagation. Among these are similarity networks [Heckerman 1991] and the related multinets [Geiger and Heckerman 1991], the use of asymmetric representations for decision making [Smith et al 1993], probabilistic Horn rules [Poole 1993], and also decision trees [Boutilier et al 1996] and decision graphs [Chickering et al 1997]. In this chapter I focus on the decision tree/decision graph approach and review it in the following for Bayesian networks.…”