Caroline L. König.
Representing Asymmetric Decision Problems with Decision Analysis Networks. Dept. Artificial Intelligence. UNED, Madrid, Spain, 2012.
Supervisors: Francisco Javier Díez Vegas and Manuel Luque Gallego.
192 pages. PDF (3.0 MB), BibTeX entry.
During the last two decades several specific decision analysis formalisms for the representation of asymmetric decision problems have been proposed as the common decision analysis formalisms, influence diagrams (IDs) and decision trees (DTs) are not able to represent asymmetric decision problems efficiently. Although those formalisms provide different solutions, none of them has been used in practice to represent real-world problems, what might be a sign that they are not simple enough to facilitate the construction of the model or the communication with the expert. The latter is very important in fields such as medicine where the expert needs to understand the system to accept its advice. For these reasons a new probabilistic graphical model, decision analysis networks (DANs) were proposed by Díez and Luque (2010), which intend to represent the asymmetric aspects of decision problems more naturally.
The main contribution of this work is a revision of DANs from the point of view of syntax and semantics regarding the representation of asymmetric aspects and a comparison of the features of DANs to the previous decision analysis formalisms. First this work presents a review of several previous formalisms and a detailed description of the approaches these formalisms take for the representation of order asymmetry and structural asymmetry, illustrating each method with the representation of three typical asymmetric decision problems taken from the literature. Secondly these alternative representations are compared with detail to the DAN representation, what makes the strengths and weaknesses of each formalism evident. This comparison led further to the improvement of the DAN formalism, because some loose ends and ambiguities were detected. After improving DANs with some refined features, DANs compare now equally or even favorably with the other decision analysis formalisms. As a result of the comparison, we confirm that DANs are a suitable decision analysis tool, first because DANs provide a natural representation of both order and structural asymmetry and second because DANs represent problems with local descriptions, which are independent from the complexity of the problem, what makes DANs suitable for the representation of many problems that cannot be represented efficiently with most of the alternative formalisms.
Finally another important contribution of this work is the implementation of DANs in OpenMarkov, an open-source software tool for the edition and evaluation of probabilistic graphical models with the objective that DANs can be used in practice for decision analysis.