Interval Influence Diagrams

TL;DR

This paper introduces an interval-based probabilistic reasoning method for influence diagrams, enabling sensitivity analysis and handling uncertain probability data efficiently.

Contribution

It develops a novel approach for influence diagrams using interval probabilities, with procedures for node removal and arc reversal that optimize bounds within constraints.

Findings

Bounds are optimal within the class of lower-bound constraints.

Storage and computational complexity are comparable to point-valued methods.

Preliminary empirical results demonstrate the approach's practicality.

Abstract

We describe a mechanism for performing probabilistic reasoning in influence diagrams using interval rather than point valued probabilities. We derive the procedures for node removal (corresponding to conditional expectation) and arc reversal (corresponding to Bayesian conditioning) in influence diagrams where lower bounds on probabilities are stored at each node. The resulting bounds for the transformed diagram are shown to be optimal within the class of constraints on probability distributions that can be expressed exclusively as lower bounds on the component probabilities of the diagram. Sequences of these operations can be performed to answer probabilistic queries with indeterminacies in the input and for performing sensitivity analysis on an influence diagram. The storage requirements and computational complexity of this approach are comparable to those for point-valued probabilistic inference mechanisms, making the approach attractive for performing sensitivity analysis and where probability information is not available. Limited empirical data on an implementation of the methodology are provided.