Higher-Order Relations Skew Link Prediction in Graphs

TL;DR

This paper investigates how higher-order relations affect link prediction heuristics like Common Neighbors, revealing that such heuristics overestimate prediction accuracy in these contexts and proposing an adjustment for better evaluation.

Contribution

It provides a theoretical analysis of the overestimation issue caused by higher-order relations and introduces an adjustment factor for more accurate link prediction evaluation.

Findings

Common Neighbors performs well with higher-order relations.

CN overestimates prediction ability in the presence of higher-order relations.

An adjustment factor improves the estimation of generalization scores.

Abstract

The problem of link prediction is of active interest. The main approach to solving the link prediction problem is based on heuristics such as Common Neighbors (CN) -- more number of common neighbors of a pair of nodes implies a higher chance of them getting linked. In this article, we investigate this problem in the presence of higher-order relations. Surprisingly, it is found that CN works very well, and even better in the presence of higher-order relations. However, as we prove in the current work, this is due to the CN-heuristic overestimating its prediction abilities in the presence of higher-order relations. This statement is proved by considering a theoretical model for higher-order relations and by showing that AUC scores of CN are higher than can be achieved from the model. Theoretical justification in simple cases is also provided. Further, we extend our observations to other similar link prediction algorithms such as Adamic Adar. Finally, these insights are used to propose an adjustment factor by taking into conscience that a random graph would only have a best AUC score of 0.5. This adjustment factor allows for a better estimation of generalization scores.