Formulation of Tradeoffs in Planning under Uncertainty

MP Wellman Research Notes in Artificial Intelligence, Pitman Publishing, 1990. Google Books

Graphical inference in qualitative probabilistic networks

Qualitative probabilistic networks (QPNs) are abstractions of influence diagrams that encode constraints on the probabilistic relation among variables rather than precise numeric distributions. Qualitative relations express monotonicity constraints on direct probabilistic relations between variables, or on interactions among the direct relations. Like their numeric counterpart, QPNs facilitate graphical inference: methods for deriving qualitative relations of interest via graphical transformations of the network model. However, query processing in QPNs exhibits computational properties quite different from basic influence diagrams. In particular, the potential for information loss due to the incomplete specification of probabilities poses the new challenge of minimizing ambiguity. Analysis of the properties of QPN transformations reveals several characteristics of admissible graphical inference procedures.

Fundamental concepts of qualitative probabilistic networks

Graphical representations for probabilistic relationships have recently received considerable attention in AI. Qualitative probabilistic networks abstract from the usual numeric representations by encoding only qualitative relationships, which are inequality constraints on the joint probability distribution over the variables. Although these constraints are insufficient to determine probabilities uniquely, they are designed to justify the deduction of a class of relative likelihood conclusions that imply useful decision-making properties. Two types of qualitative relationship are defined, each a probabilistic form of monotonicity constraint over a group of variables. Qualitative influences describe the direction of the relationship between two variables. Qualitative synergies describe interactions among influences. The probabilistic definitions chosen justify sound and efficient inference procedures based on graphical manipulations of the network. These procedures answer queries about qualitative relationships among variables separated in the network and determine structural properties of optimal assignments to decision variables.