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A hidden challenge of link prediction: which pairs to check?

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Abstract

The traditional setup of link prediction in networks assumes that a test set of node pairs, which is usually balanced, is available over which to predict the presence of links. However, in practice, there is no test set: the ground truth is not known, so the number of possible pairs to predict over is quadratic in the number of nodes in the graph. Moreover, because graphs are sparse, most of these possible pairs will not be links. Thus, link prediction methods, which often rely on proximity-preserving embeddings or heuristic notions of node similarity, face a vast search space, with many pairs that are in close proximity, but that should not be linked. To mitigate this issue, we introduce LinkWaldo, a framework for choosing from this quadratic, massively skewed search space of node pairs, a concise set of candidate pairs that, in addition to being in close proximity, also structurally resemble the observed edges. This allows it to ignore some high-proximity but low-resemblance pairs, and also identify high-resemblance, lower-proximity pairs. Our framework is built on a model that theoretically combines stochastic block models (SBMs) with node proximity models. The block structure of the SBM maps out where in the search space new links are expected to fall, and the proximity identifies the most plausible links within these blocks, using locality sensitive hashing to avoid expensive exhaustive search. LinkWaldo can use any node representation learning or heuristic definition of proximity and can generate candidate pairs for any link prediction method, allowing the representation power of current and future methods to be realized for link prediction in practice. We evaluate LinkWaldo on 13 networks across multiple domains and show that on average it returns candidate sets containing 7–33% more missing and future links than both embedding-based and heuristic baselines’ sets. Our code is available at https://github.com/GemsLab/LinkWaldo.

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Acknowledgements

This work is an invited extension of a paper accepted at ICDM 2020 [4] and is supported by an NSF Graduate Research Fellowship, NSF CAREER Grant No. IIS 1845491, Army Young Investigator Award No. W9–11NF1810397, and an Amazon faculty award. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation or other funding parties.

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  1. Computer Science & Engineering, University of Michigan, Ann Arbor, USA

    Caleb Belth, Alican Büyükçakır & Danai Koutra

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  1. Caleb Belth
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  2. Alican Büyükçakır
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  3. Danai Koutra
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Correspondence to Caleb Belth.

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Proximity models

Proximity models

Here we discuss the proximity models used in Sect. 5.1. The proximity model for each method (along with parameters for the NMF+Bag baseline) is given in Table 6. We observe that the AA heuristic performed well on several datasets. During development, we tried over two dozen embedding methods (including GNNs) and found NetMF to be the most consistently strong for both LaPM and LinkWaldo. This, combined with the strong performance of AA, suggests that there is much room for improving proximity-preserving embedding methods. Improving their performance for low-degree nodes is of particular importance, as discussed in Sect. 5.4.

Table 6 The best input proximity model for LaPM and LinkWaldo (used in Sect. 5.1) and parameter deviations from default for NMF+Bag
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Belth, C., Büyükçakır, A. & Koutra, D. A hidden challenge of link prediction: which pairs to check?. Knowl Inf Syst 64, 743–771 (2022). https://doi.org/10.1007/s10115-021-01632-x

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