Interval influence diagrams.

*(English)*Zbl 0721.68061
Uncertainty in artificial intelligence, 5th Workshop, Ontario/Canada 1989, Mach. Intell. Pattern Recognition 10, 149-161 (1990).

[For the entire collection see Zbl 0718.68001.]

The paper describes a mechanism for performing probabilistic reasoning in influence diagrams using interval rather than point-valued probabilities. Imprecision is incorporated in probability values by specifying lower bounds on input probabilities and using influence diagrams as a means of expressing conditional independence. The characterization of constraints as lower bounds allows to derive a relatively efficient procedure for probabilistic inference, based on successive transformations to the diagrams, at the cost of some expressiveness. The implications of these transformations in terms of the sets of probability distributions admitted by the bounds are analysed in detail. Replacing precise probability distributions by lower bounds on the conditional probability distributions associated with each node in the network, the fundamental transformations to an influence diagram (node removal and arc reversal) describe a diagram transformation from one topology to another, and updates the bounds for relevant nodes in the diagram. There are proved soundness and minimality theorems on these transformations, being obtained weaker bounds as successive transformations when applied to a diagram. The approach is efficient in terms of storage and computation, and the operations performed are optimal with respect to constraints expressed as lower bounds.

The paper describes a mechanism for performing probabilistic reasoning in influence diagrams using interval rather than point-valued probabilities. Imprecision is incorporated in probability values by specifying lower bounds on input probabilities and using influence diagrams as a means of expressing conditional independence. The characterization of constraints as lower bounds allows to derive a relatively efficient procedure for probabilistic inference, based on successive transformations to the diagrams, at the cost of some expressiveness. The implications of these transformations in terms of the sets of probability distributions admitted by the bounds are analysed in detail. Replacing precise probability distributions by lower bounds on the conditional probability distributions associated with each node in the network, the fundamental transformations to an influence diagram (node removal and arc reversal) describe a diagram transformation from one topology to another, and updates the bounds for relevant nodes in the diagram. There are proved soundness and minimality theorems on these transformations, being obtained weaker bounds as successive transformations when applied to a diagram. The approach is efficient in terms of storage and computation, and the operations performed are optimal with respect to constraints expressed as lower bounds.

Reviewer: N.Curteanu (Iaşi)

##### MSC:

68T27 | Logic in artificial intelligence |

03B47 | Substructural logics (including relevance, entailment, linear logic, Lambek calculus, BCK and BCI logics) |