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Transfer Learning on Edge Connecting Probability Estimation Under Graphon Model
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Proposes GTrans, a transfer learning method for graphon estimation without known node correspondence that aligns a small target graph to a larger source graph via (entropic) Gromov-Wasserstein optimal transport on neighborhood-smoothed estimates, with a residual-smoothing debiasing step to avoid negative transfer.
Problem
Estimating connection probabilities (graphon) for a small target graph is inaccurate; existing transfer methods need known node correspondences between source and target graphs.
Approach
Align source and target nodes by Gromov-Wasserstein/entropic GW coupling computed on neighborhood-smoothed initial graphon estimates (not noisy adjacency matrices), project the source estimate through the coupling, and add an adaptive residual-smoothing correction when the GW distance between graphons is large.
Key results
- On IMDB-Binary, GTrans-EGW reaches 77.50% accuracy (transfer from COLLAB), outperforming the best listed baseline by roughly 2-5 points.
- On PROTEINS-Full transferring from D&D, GTrans-GW reaches 69.33% versus 63-65% for graphon baselines like NS, USVT, SAS.
- In synthetic experiments with n_t=50 and n_s=500, GTrans-GW/EGW achieve lower MSE than NS, USVT, ICE, and SAS on most graphon pairs, e.g. 0.9 vs 2.1 for NS on 7->6.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Transfer graphon information from Reddit-B using GW alignment | GTrans · IMDB-Binary | accuracy: 74.30 ± 2.16 -> 76.30 ± 2.35 | Helped |
| Use entropic GW instead of GW for transfer from Reddit-B | GTrans · IMDB-Binary | accuracy: 76.30 ± 2.35 -> 76.80 ± 1.52 | Helped |
| Transfer graphon information from COLLAB using GW alignment | GTrans · IMDB-Binary | accuracy: 75.30 ± 2.19 -> 76.25 ± 2.06 | Helped |
| Use entropic GW instead of GW for transfer from COLLAB | GTrans · IMDB-Binary | accuracy: 76.25 ± 2.06 -> 77.50 ± 2.13 | Helped |
| Transfer graphon information from Reddit-B using GW alignment | GTrans · IMDB-Multi | accuracy: 49.13 ± 3.04 -> 49.10 ± 1.33 | Helped |
| Use entropic GW instead of GW for transfer from Reddit-B | GTrans · IMDB-Multi | accuracy: 49.10 ± 1.33 -> 51.27 ± 1.98 | Helped |
| Transfer graphon information from COLLAB using GW alignment | GTrans · IMDB-Multi | accuracy: 48.00 ± 2.93 -> 50.47 ± 1.42 | Helped |
| Use entropic GW instead of GW for transfer from COLLAB | GTrans · IMDB-Multi | accuracy: 50.47 ± 1.42 -> 50.23 ± 0.92 | No clear effect |
| Transfer graphon information from D&D using GW alignment | GTrans · PROTEINS-Full | accuracy: 70.11 ± 2.12 -> 69.33 ± 2.55 | Hurt |
| Use entropic GW instead of GW for transfer from D&D | GTrans · PROTEINS-Full | accuracy: 69.33 ± 2.55 -> 68.52 ± 1.59 | Hurt |
| Increase source graph size | GTrans-GW and GTrans-EGW · Synthetic graphons 1–10; target size 50 | MSE | Helped |
| Transfer between dissimilar graphons with adaptive debiasing | GTrans · Synthetic graphon pairs with large difference | MSE | No clear effect |
Surprising findings
- When the target graph is sparse, transferring from a slightly denser source works better than from an equally sparse-shifted one, and an extremely sparse source can yield a near-zero initial estimate that limits transfer.
- On some dissimilar graphon pairs (e.g., 8->9), GTrans performs no better than or worse than target-only baselines such as ICE.
Limitations
- Assumes a single source graph; multiple sources not handled.
- Designed only for static graphs; no node covariates are used.
- Stability theorem requires an entropic regularization lower bound and a small-perturbation cutoff; the GW-based theorem is only local.
Experimental setup
Datasets: IMDB-Binary IMDB-MULTI COLLAB Reddit-Binary D&D PROTEINS-Full
Benchmarks: IMDB-Binary IMDB-MULTI PROTEINS-Full synthetic graphons 1-10
Metrics: MSE test accuracy
Baselines: neighborhood smoothing sorting and smoothing universal singular value thresholding iterative connecting probability estimation GWB IGNR SIGL graphlet kernel
Builds on: neighborhood smoothing entropic Gromov-Wasserstein G-Mixup
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