Minority Representation in Network Rankings: Methods for Estimation, Testing, and Fairness

Music City Center 

Networks, composed of nodes and connections, are widely used to model relationships across various fields. Centrality metrics, vital for assessing node importance, inform decisions such as identifying key nodes or prioritizing resources. However, networks often suffer from noise, such as missing or incorrect edges, which can distort centrality-based decisions. Specifically, if edge noise is driven by label information, it can lead to unfair decision-making, distorting the representation of certain groups, such as minorities. To address this, we focus on networks with label information and introduce a formal definition of minority representation, defined as the proportion of minority nodes among the top-ranked nodes. We model systematic bias using label-related missing edge errors. We propose methods to estimate and test bias parameters under various noisy scenarios. Asymptotic limits of minority representation statistics are derived under specific network models and used to uncover de-biased representations. Simulation results demonstrate the effectiveness of our estimation, testing, and correction procedures. We apply our methods to a contact network, showcasing applicability.

Contact networks

Graphon model

Noisy networks

Stochastic block model

Systematic bias 

Section on Statistical Learning and Data Science