Towards Precision of Probabilistic Bounds Propagation

TL;DR

This paper introduces the DUCK-calculus, a method for efficiently propagating probabilistic bounds that maintains uncertain rules and independences, providing precise analytical bounds for probabilistic entailment.

Contribution

It presents a novel probabilistic calculus that combines local bounds propagation with simple operations research techniques for improved precision.

Findings

Provides new precise analytical bounds for probabilistic entailment

Demonstrates efficient incremental maintenance of uncertain probabilistic rules

Combines deductive database evaluation with operations research methods

Abstract

The DUCK-calculus presented here is a recent approach to cope with probabilistic uncertainty in a sound and efficient way. Uncertain rules with bounds for probabilities and explicit conditional independences can be maintained incrementally. The basic inference mechanism relies on local bounds propagation, implementable by deductive databases with a bottom-up fixpoint evaluation. In situations, where no precise bounds are deducible, it can be combined with simple operations research techniques on a local scope. In particular, we provide new precise analytical bounds for probabilistic entailment.