Constraint Propagation with Imprecise Conditional Probabilities
This work addresses a specific challenge in probabilistic reasoning for AI and decision-making systems, offering incremental improvements over existing methods like linear programming.
The paper tackles the problem of reasoning with default rules when only imprecise conditional probabilities are available, proposing an iterative procedure that provides improved bounds for conditional probabilities without requiring independence assumptions.
An approach to reasoning with default rules where the proportion of exceptions, or more generally the probability of encountering an exception, can be at least roughly assessed is presented. It is based on local uncertainty propagation rules which provide the best bracketing of a conditional probability of interest from the knowledge of the bracketing of some other conditional probabilities. A procedure that uses two such propagation rules repeatedly is proposed in order to estimate any simple conditional probability of interest from the available knowledge. The iterative procedure, that does not require independence assumptions, looks promising with respect to the linear programming method. Improved bounds for conditional probabilities are given when independence assumptions hold.