Optimal Upper and Lower Bounds for Boolean Expressions by Dissociation

TL;DR

This paper introduces a method to compute tight upper and lower probability bounds for Boolean expressions by dissociating variables, generalizing existing techniques like node splitting and variable renaming.

Contribution

It provides a theoretical framework for optimal dissociation bounds, extending previous approaches in probabilistic reasoning and database query evaluation.

Findings

Proves the optimality of the assigned probabilities for dissociated variables.

Generalizes existing dissociation techniques such as node splitting.

Offers a unified approach for bounding Boolean expression probabilities.

Abstract

This paper develops upper and lower bounds for the probability of Boolean expressions by treating multiple occurrences of variables as independent and assigning them new individual probabilities. Our technique generalizes and extends the underlying idea of a number of recent approaches which are varyingly called node splitting, variable renaming, variable splitting, or dissociation for probabilistic databases. We prove that the probabilities we assign to new variables are the best possible in some sense.