When do Numbers Really Matter?

TL;DR

This paper investigates the sensitivity of probabilistic queries in belief networks to small parameter changes, providing bounds and conditions that determine when such variations significantly impact query results.

Contribution

It offers the first analytical bounds on how parameter changes affect probabilistic queries, clarifying when small variations matter or are negligible.

Findings

Derived tight bounds on query sensitivity to parameter changes

Identified scenarios where parameter variations significantly impact results

Explained robustness of belief networks against small parameter perturbations

Abstract

Common wisdom has it that small distinctions in the probabilities (parameters) quantifying a belief network do not matter much for the results of probabilistic queries. Yet, one can develop realistic scenarios under which small variations in network parameters can lead to significant changes in computed queries. A pending theoretical question is then to analytically characterize parameter changes that do or do not matter. In this paper, we study the sensitivity of probabilistic queries to changes in network parameters and prove some tight bounds on the impact that such parameters can have on queries. Our analytic results pinpoint some interesting situations under which parameter changes do or do not matter. These results are important for knowledge engineers as they help them identify influential network parameters. They also help explain some of the previous experimental results and observations with regards to network robustness against parameter changes.