From Influence Diagrams to Junction Trees

Jensen, Frank; Jensen, Finn Verner; Dittmer, Sören

doi:10.1016/b978-1-55860-332-5.50051-1

Cited by 127 publications

(100 citation statements)

References 9 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…. Other and more efficient methods have been constructed (Shachter, 1986;Shenoy, 1992;Jensen et al, 1994), and the interested reader can find them in the textbooks (Jensen and Nielsen, 2007;Kjaerulff and Madsen, 2008).…”

Section: Evaluating Influence Diagramsmentioning

confidence: 99%

“…Exact algorithms for solving influence diagrams range from algorithms working directly on the influence diagram structure (Shachter, 1986) to algorithms that rely on a secondary representation of the model. 2 Examples of the latter include search-based algorithms that operate on a decision tree representation of the model (Yuan and Wu, 2010;Yuan et al, 2010), message-passing algorithms that rely on a junction tree representation of the model (Jensen et al, 1994;Madsen and Jensen, 1999;Madsen and Nilsson, 2001), and algorithms that transform the influence diagram into a so-called decision circuit (Bhattacharjya and Shachter, 2007;Shachter and Bhattacharjya, 2010), the analogue to arithmetic circuits for Bayesian networks (Darwiche, 2003). The computational difficulties involved in solving influence diagrams have also sparked the development of several approximate algorithms.…”

Section: Other Issuesmentioning

confidence: 99%

See 1 more Smart Citation

Probabilistic decision graphs for optimization under uncertainty

Jensen

Nielsen

2013

Ann Oper Res

Self Cite

View full text Add to dashboard Cite

This paper provides a survey on probabilistic decision graphs for modeling and solving decision problems under uncertainty. We give an introduction to influence diagrams, which is a popular framework for representing and solving sequential decision problems with a single decision maker. As the methods for solving influence diagrams can scale rather badly in the length of the decision sequence, we present a couple of approaches for calculating approximate solutions.The modeling scope of the influence diagram is limited to so-called symmetric decision problems. This limitation has motivated the development of alternative representation languages, which enlarge the class of decision problems that can be modeled efficiently. We present some of these alternative frameworks and demonstrate their expressibility using several examples. Finally, we provide a list of software systems that implement the frameworks described in the paper.

show abstract

Section: Evaluating Influence Diagramsmentioning

confidence: 99%

Section: Other Issuesmentioning

confidence: 99%

Probabilistic decision graphs for optimization under uncertainty

Jensen

Nielsen

2013

Ann Oper Res

Self Cite

View full text Add to dashboard Cite

show abstract

“…One advantage of this algorithm is that it can be based on any belief-updating algorithm for BNs. Other techniques to solve influence diagrams were offered by Jensen, Jensen and Dittmer [19] and Madsen and Jensen [21].…”

Section: Introductionmentioning

confidence: 99%

An Efficient Exhaustive Anytime Sampling Algorithm for Influence Diagrams

García-Sánchez

Drużdżel

2007

Advances in Probabilistic Graphical Models

View full text Add to dashboard Cite

Summary.We describe an efficient sampling algorithm for solving influence diagrams that achieves its efficiency by testing candidate decision strategies against the same set of samples and, effectively, reusing samples for each of the strategies. We show how by following this procedure we not only save a significant amount of computation but also produce better quality anytime behavior. Our algorithm is exhaustive in the sense of computing the expected utility of each of the possible decision strategies.

show abstract

“…Fast routines to compute expected utilities and identify optimal decisions that exploit the underlying graph have been defined for a long while (e.g., Jensen et al 1994, Shachter 1986). However, these are almost exclusively designed to work when the utility can be assumed to factorize additively, i.e., assuming that the utility can be written as a linear combination of smaller dimensional functions over disjoint subsets of the decision problem's attributes.…”

Section: Introductionmentioning

confidence: 99%

Directed Expected Utility Networks

Leonelli

Smith

2017

Decision Analysis

View full text Add to dashboard Cite

Abstract.A variety of statistical graphical models have been defined to represent the conditional independences underlying a random vector of interest. Similarly, many different graphs embedding various types of preferential independences, such as, for example, conditional utility independence and generalized additive independence, have more recently started to appear. In this paper, we define a new graphical model, called a directed expected utility network, whose edges depict both probabilistic and utility conditional independences. These embed a very flexible class of utility models, much larger than those usually conceived in standard influence diagrams. Our graphical representation and various transformations of the original graph into a tree structure are then used to guide fast routines for the computation of a decision problem's expected utilities. We show that our routines generalize those usually utilized in standard influence diagrams' evaluations under much more restrictive conditions. We then proceed with the construction of a directed expected utility network to support decision makers in the domain of household food security.

show abstract

From Influence Diagrams to Junction Trees

Cited by 127 publications

References 9 publications

Probabilistic decision graphs for optimization under uncertainty

Probabilistic decision graphs for optimization under uncertainty

An Efficient Exhaustive Anytime Sampling Algorithm for Influence Diagrams

Directed Expected Utility Networks

Contact Info

Product

Resources

About