Post-selection inference for network structure

2026-06-30

AI Summary

This study addresses the challenge of performing valid statistical inference on connection densities among adaptively selected groups from network data, a task where conventional methods often fail. The authors propose two general approaches for constructing post-selection confidence intervals: one grounded in the framework of Berk et al., and another leveraging Talagrand-type concentration inequalities for empirical processes. Both methods ensure simultaneous coverage validity across all non-degenerate group pairs while maintaining computational scalability, with the latter achieving asymptotically optimal interval width. Empirical analyses reveal that, after properly correcting for selection effects, homophily in social networks and the hub-and-spoke structure in trade networks remain statistically significant, whereas evidence for market segmentation in labor mobility networks no longer holds.

Abstract

Researchers often use the density of connections between groups of agents, such as communities, blocs, or markets, to characterize the structure of a social or economic network. In many cases, these groups are selected using the network data, making conventional fixed-group inference procedures potentially invalid. To address this issue, we develop two new confidence intervals that are universally valid post-selection in the sense that they guarantee simultaneous coverage asymptotically over all pairs of groups whose relative sizes do not vanish. Our first interval builds on a strategy of \cite{berk2013valid}. Our second interval is based on a Talagrand-type concentration inequality for empirical processes. Both intervals are simple to compute and scalable to large networks, but a key technical contribution of our paper is show that only the second interval achieves the best-possible width asymptotically up to a constant factor. Three empirical illustrations show that accounting for selection can matter in practice. Some evidence for homophily in a social network and a hub-and-spoke structure in a trade network survives our correction, while evidence for disjoint market segments in a worker transition network does not.

Problem

• post-selection inference
• network structure
• group selection
• statistical validity
• confidence intervals

Innovation

• post-selection inference
• network structure
• confidence intervals
• Talagrand concentration inequality
• asymptotic optimality