Exploiting Evidence-dependent Sensitivity Bounds

TL;DR

This paper introduces evidence-dependent bounds on sensitivity analysis in probabilistic networks, enabling efficient identification of influential parameters without exhaustive computation across all evidence profiles.

Contribution

It develops properties of sensitivity functions based solely on evidence probability, providing bounds and regions for sensitivity values independent of specific network details.

Findings

Establishes upper bounds on parameter sensitivity values.

Identifies regions where sensitivity function vertices are located.

Enables pre-analysis screening of influential parameters.

Abstract

Studying the effects of one-way variation of any number of parameters on any number of output probabilities quickly becomes infeasible in practice, especially if various evidence profiles are to be taken into consideration. To provide for identifying the parameters that have a potentially large effect prior to actually performing the analysis, we need properties of sensitivity functions that are independent of the network under study, of the available evidence, or of both. In this paper, we study properties that depend upon just the probability of the entered evidence. We demonstrate that these properties provide for establishing an upper bound on the sensitivity value for a parameter; they further provide for establishing the region in which the vertex of the sensitivity function resides, thereby serving to identify parameters with a low sensitivity value that may still have a large impact on the probability of interest for relatively small parameter variations.