Pairwise Learning for Neural Link Prediction
Abstract
In this paper, we aim at providing an effective Pairwise Learning for Neural Link Prediction (PLNLP) framework. The framework treats link prediction as a pairwise learning to rank problem and consists of four main components, i.e., neighborhood encoder, link predictor, negative sampler and objective function. The framework is flexible that any generic graph neural convolutions or link prediction specific neural architectures could be employed as neighborhood encoder. For link predictor, we design different scoring functions, which could be selected based on different types of graphs. In negative sampler, we provide several sampling strategies, which are problem specific. As for objective function, we propose to use an effective ranking loss, which approximately maximizes the standard ranking metric AUC. We evaluate the proposed PLNLP framework on 4 link property prediction datasets of Open Graph Benchmark (OGB), including ogbl-ddi, ogbl-collab, ogbl-ppa and ogbl-ciation2. PLNLP achieves top 1 performance on ogbl-ddi and ogbl-collab, and top 2 performance on ogbl-ciation2 only with basic neural architecture. The experimental results demonstrate the effectiveness of PLNLP.
Benchmark Results
Tested on 4 datasets 1 baseline value reported too low
Tables show presented results in global context (best 3 papers + GCN + MLP).
OGB
| # | Model | Hits@50 ↑ | Paper |
|---|---|---|---|
| 1 | PROXI | 0.7650
±0.0027 | |
| 2 | OGB Leader | 0.7129
±0.0018 | |
| 3 | GIDN | 0.7096
±0.0055 | |
| 4 | PLNLP | 0.7059
±0.0029 | This paper |
| 5 | HOP-Rec | 0.7012
±0.0016 | This paper |
| 9 | GCN | 0.6621
±0.0033 best reported | best at pub: OGB (NeurIPS 2020) best today: On the Impact of Feature Heterophily on Link Prediction with Graph Neural Networks (NeurIPS 2024) |
| 16 | AA+Proposal Set | 0.6548 | This paper |
| 20 | SEAL | 0.6474
±0.0033 | This paper |
| 23 | AA | 0.6435 best reported | best at pub: Labeling Trick: A Theory of Using Graph Neural Networks for Multi-Node Representation Learning (NeurIPS 2020) best today: On the Impact of Feature Heterophily on Link Prediction with Graph Neural Networks (NeurIPS 2024) |
| 27 | CN | 0.6137 | This paper |
| 28 | SAGE | 0.5944
±0.0137 best reported | best today: PROXI: Challenging the GNNs for Link Prediction (TMLR 2024) |
| 41 | GraphSAGE | 0.5463
±0.0112 | |
| 60 | DeepWalk | 0.5040
±0.0030 best reported | best at pub: Formatting Instructions for ICLR 2021 Conference Submissions (2020) Difference within reported uncertainty; not counted as underperformance. |
| 68 | Node2Vec | 0.4929
±0.0064 best reported | best at pub: Formatting Instructions for ICLR 2021 Conference Submissions (2020) best today: Asymmetric Learning for Graph Neural Network based Link Prediction (2023) Difference within reported uncertainty; not counted as underperformance. |
| 94 | MLP | 0.4438
±0.0347 | |
| 98 | MF | 0.4181
±0.0167 best reported | best at pub: Formatting Instructions for ICLR 2021 Conference Submissions (2020) best today: PROXI: Challenging the GNNs for Link Prediction (TMLR 2024) |
| # | Model | Hits@20 ↑ | Paper |
|---|---|---|---|
| 1 | ELGNN | 0.9777
±0.0037 | |
| 2 | GIDN | 0.9542 | |
| 3 | AGDN | 0.9538
±0.0094 | |
| 5 | PLNLP | 0.9088
±0.0313 | This paper |
| 8 | SAGE+Edge Attr | 0.8781
±0.0447 | This paper |
| 10 | CFLP (w/ JKNet) | 0.8608
±0.0198 | This paper |
| 19 | SAGE+Proposal Set | 0.7495
±0.0317 | This paper |
| 20 | SAGE | 0.6719
±0.0118 best reported | best today: Link Prediction with Untrained Message Passing Layers (2024) |
| 24 | GCN | 0.6476
±0.0145 best reported | best at pub: OGB (NeurIPS 2020) best today: Link Prediction with Untrained Message Passing Layers (2024) |
| 25 | Node2Vec | 0.6363
±0.0205 best reported | best at pub: Formatting Instructions for ICLR 2021 Conference Submissions (2020) best today: Link Prediction with Untrained Message Passing Layers (2024) |
| 31 | MF | 0.5950
±0.0168 best reported | best at pub: Formatting Instructions for ICLR 2021 Conference Submissions (2020) best today: Link Prediction with Untrained Message Passing Layers (2024) |
| 38 | GraphSAGE | 0.5390
±0.0474 | |
| 43 | SEAL | 0.4974
±0.0239 best reported | best at pub: Labeling Trick: A Theory of Using Graph Neural Networks for Multi-Node Representation Learning (NeurIPS 2020) best today: Link Prediction with Untrained Message Passing Layers (2024) |
| 50 | AA | 0.3975 best reported | best at pub: Labeling Trick: A Theory of Using Graph Neural Networks for Multi-Node Representation Learning (NeurIPS 2020) best today: Link Prediction with Untrained Message Passing Layers (2024) |
| 51 | CN | 0.3869 best reported | best at pub: Labeling Trick: A Theory of Using Graph Neural Networks for Multi-Node Representation Learning (NeurIPS 2020) best today: Link Prediction with Untrained Message Passing Layers (2024) |
| 65 | DeepWalk | 0.2640
±0.0610 best reported | best at pub: Formatting Instructions for ICLR 2021 Conference Submissions (2020) Difference within reported uncertainty; not counted as underperformance. |
| # | Model | Hits@100 ↑ | Paper |
|---|---|---|---|
| 1 | OGB Leader | 0.6524
±0.0150 | |
| 2 | PRB | 0.6347
±0.0175 | |
| 3 | LPFormer | 0.6332
±0.0063 | |
| 9 | RA | 0.5324 | This paper |
| 14 | SAGE | 0.5013
±0.0055 best reported | best today: Asymmetric Learning for Graph Neural Network based Link Prediction (2023) |
| 19 | SEAL | 0.4880
±0.0316 | This paper |
| 23 | MLP | 0.4600 | |
| 39 | AA | 0.3245 | This paper |
| 41 | PLNLP | 0.3238
±0.0258 | This paper |
| 42 | MF | 0.3230
±0.0090 best reported | best at pub: Formatting Instructions for ICLR 2021 Conference Submissions (2020) Difference within reported uncertainty; not counted as underperformance. |
| 45 | GCN | 0.3084
±0.0178 best reported | best at pub: Formatting Instructions for ICLR 2021 Conference Submissions (2020) best today: Link Prediction with Untrained Message Passing Layers (2024) |
| 46 | DeepWalk | 0.2890
±0.0150 best reported | best at pub: Formatting Instructions for ICLR 2021 Conference Submissions (2020) |
| 49 | CN | 0.2765 | prev best: Labeling Trick: A Theory of Using Graph Neural Networks for Multi-Node Representation Learning (NeurIPS 2020) |
| 57 | Node2Vec | 0.2230
±0.0080 best reported | best at pub: Formatting Instructions for ICLR 2021 Conference Submissions (2020) Difference within reported uncertainty; not counted as underperformance. |
| 64 | Classification | 0.1655 | This paper |
| 63 | GraphSAGE | 0.1655
±0.0240 |
| # | Model | MRR ↑ | Paper |
|---|---|---|---|
| 1 | CFG | 0.8997
±0.0015 | |
| 2 | SIEG | 0.8987
±0.0018 | |
| 3 | LPFormer | 0.8981
±0.0013 | |
| 8 | SEAL | 0.8767
±0.0032 | This paper |
| 12 | GCN | 0.8705
±0.0004 best reported | best at pub: OGB (NeurIPS 2020) best today: On the Impact of Feature Heterophily on Link Prediction with Graph Neural Networks (NeurIPS 2024) |
| 20 | PLNLP | 0.8492
±0.0029 | This paper |
| 23 | Classification | 0.8464 | This paper |
| 30 | SAGE | 0.8292
±0.0022 best reported | best today: Weak Models Can be Good Teachers: A Case Study on Link Prediction with MLPs (2025) Difference within reported uncertainty; not counted as underperformance. |
| 32 | GraphSAGE | 0.8264
±0.0001 | |
| 52 | AA | 0.7596 best reported | best at pub: Labeling Trick: A Theory of Using Graph Neural Networks for Multi-Node Representation Learning (NeurIPS 2020) best today: Weak Models Can be Good Teachers: A Case Study on Link Prediction with MLPs (2025) |
| 54 | CN | 0.7430 best reported | best at pub: Labeling Trick: A Theory of Using Graph Neural Networks for Multi-Node Representation Learning (NeurIPS 2020) best today: Weak Models Can be Good Teachers: A Case Study on Link Prediction with MLPs (2025) |
| 62 | MF | 0.5186
±0.0443 | This paper |
| 71 | MLP | 0.3917
±0.0044 |
