Constraint Propagation with Imprecise Conditional Probabilities

TL;DR

This paper introduces a method for reasoning with default rules under uncertainty by propagating bounds on conditional probabilities, avoiding independence assumptions and improving bounds with such assumptions.

Contribution

It presents a local uncertainty propagation approach for estimating conditional probabilities without relying on independence assumptions.

Findings

Provides a procedure for bounding conditional probabilities using local propagation rules.

Avoids the need for independence assumptions in probability estimation.

Offers improved bounds when independence assumptions are valid.

Abstract

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.