Conformal Link Prediction with False Discovery Rate Control

TL;DR

This paper introduces a novel conformal link prediction method that controls the false discovery rate in network analysis, effectively handling complex dependencies and unknown missing data patterns with theoretical guarantees.

Contribution

The paper presents a distribution-free conformal link prediction approach with a new multi-splitting and e-value aggregation scheme for FDR control in complex networks.

Findings

Method achieves valid FDR control under unknown missing mechanisms.

Applicable to various network types without assumptions on missing rates.

Demonstrates robustness and effectiveness through simulations and real data.

Abstract

We propose a new method for predicting multiple missing links in partially observed networks while controlling the false discovery rate (FDR), a largely unresolved challenge in network analysis. The main difficulty lies in handling complex dependencies and unknown, heterogeneous missing patterns. We introduce conformal link prediction ({\tt clp}), a distribution-free procedure grounded in the exchangeability structure of weighted graphon models. Our approach constructs conformal p-values via a novel multi-splitting strategy that restores exchangeability within local test sets, thereby ensuring valid row-wise FDR control, even under unknown missing mechanisms. To achieve FDR control across all missing links, we further develop a new aggregation scheme based on e-values, which accommodates arbitrary dependence across network predictions. Our method requires no assumptions on the missing rates, applies to weighted, unweighted, undirected, and bipartite networks, and enjoys finite-sample theoretical guarantees. Extensive simulations and real-world data study confirm the effectiveness and robustness of the proposed approach.