[Paper Review] Discriminating abilities of threshold-free evaluation metrics in link prediction

Tao Zhou|arXiv (Cornell University)|May 10, 2022

Bioinformatics and Genomic Networks4 citations

TL;DR

This paper proposes a framework to evaluate the discriminating ability of threshold-free metrics in link prediction using a tunable toy model with adjustable noise and predictability. It finds that AUC and AUPR significantly outperform balanced precision (BP), with AUC being slightly more discriminating than AUPR, suggesting AUC and AUPR should be used together while BP alone may yield misleading evaluations.

ABSTRACT

Link prediction is a paradigmatic and challenging problem in network science, which attempts to uncover missing links or predict future links, based on known topology. A fundamental but still unsolved issue is how to choose proper metrics to fairly evaluate prediction algorithms. The area under the receiver operating characteristic curve (AUC) and the balanced precision (BP) are the two most popular metrics in early studies, while their effectiveness is recently under debate. At the same time, the area under the precision-recall curve (AUPR) becomes increasingly popular, especially in biological studies. Based on a toy model with tunable noise and predictability, we propose a method to measure the discriminating abilities of any given metric. We apply this method to the above three threshold-free metrics, showing that AUC and AUPR are remarkably more discriminating than BP, and AUC is slightly more discriminating than AUPR. The result suggests that it is better to simultaneously use AUC and AUPR in evaluating link prediction algorithms, at the same time, it warns us that the evaluation based only on BP may be unauthentic. This article provides a starting point towards a comprehensive picture about effectiveness of evaluation metrics for link prediction and other classification problems.

Motivation & Objective

• To address the unresolved challenge of selecting appropriate evaluation metrics for link prediction algorithms.
• To assess the discriminating power of widely used threshold-free metrics—AUC, AUPR, and BP—under controlled conditions.
• To develop a systematic method for measuring how effectively metrics distinguish between true and false links in network prediction.
• To provide empirical guidance on metric selection to ensure fair and reliable evaluation of link prediction performance.

Proposed method

• A tunable toy model is constructed to simulate networks with controllable levels of noise and predictability.
• The model generates synthetic link prediction tasks where ground-truth links are known, enabling controlled evaluation.
• The discriminating ability of each metric is quantified by measuring its sensitivity to changes in predictability and noise.
• Metrics are evaluated across multiple parameter settings to assess consistency and discriminative power.
• Statistical analysis compares the variance and sensitivity of AUC, AUPR, and BP across the model's parameter space.
• The framework enables direct comparison of metric performance in distinguishing high-quality from low-quality predictions.

Experimental results

Research questions

• RQ1 How do AUC, AUPR, and BP compare in their ability to discriminate between high-quality and low-quality link prediction results?
• RQ2 Does the discriminating power of these metrics vary with noise levels and predictability in network structures?
• RQ3 Is balanced precision (BP) a reliable metric for evaluating link prediction performance, or does it fail to distinguish meaningful differences?
• RQ4 How does the performance of AUC compare to AUPR in terms of sensitivity to changes in network predictability?
• RQ5 Can a systematic method be developed to evaluate the discriminating ability of any threshold-free evaluation metric?

Key findings

• AUC demonstrates the highest discriminating ability among the three metrics, outperforming both AUPR and BP.
• AUPR shows significantly stronger discriminating power than BP, indicating BP is less sensitive to meaningful performance differences.
• BP exhibits poor discriminating ability, suggesting evaluations based solely on BP may be unauthentic or misleading.
• The proposed method successfully quantifies and compares the sensitivity of metrics to changes in network predictability and noise.
• AUC and AUPR are recommended for simultaneous use in evaluation, as they provide more robust and reliable performance assessment than BP alone.