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Hypergraph Representation Learning with Hyperlink Random Effects

NeurIPS 2026 · Probabilistic and scientific modeling › Molecules and proteins · approach: Probabilistic embeddings and relational inference · 0 citations (OpenAlex)

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Proposes a low-rank hypergraph representation framework with hyperlink random effects (categorical, Gaussian-mixture, score-based SDE) that handles non-uniform hyperlinks, with identifiability and recovery theory plus EM-based estimation.

Problem

Learning interpretable low-rank node representations for general non-uniform hypergraphs whose hyperlinks arise from heterogeneous latent formation mechanisms.

Approach

Model each node-inclusion indicator as Bernoulli with logit f_j^T z_i + alpha_i, where each hyperlink has a latent random effect f_j drawn from a flexible distribution (finite mixture, Gaussian mixture, or score-based SDE prior), giving identifiable low-rank embeddings fit by EM-type algorithms.

Key results

• On Food Recipe cold-start, HRL-GM reaches AUC 0.827 vs 0.789 for the best baseline MultiVAE.
• On t-mixture simulated data (df=4), HRL-Score attains ARI ~0.95 while HRL-Cat, HRL-GM and HRL-Fixed stay near 0.34.
• On MovieLens cold-start, HRL-GM attains AUC 0.783 and AUPRC 0.712, outperforming all baselines.

Surprising findings

• Categorical and Gaussian-mixture random effects fail to recover group structure under heavy-tailed t-mixture random effects, while the score-based variant succeeds.

Limitations

• Relies on a low-rank latent structure; sensitivity to model misspecification not studied.
• EM algorithms may be sensitive to initialization and local optima.
• HRL-Score depends on Monte Carlo approximations; framework limited to a single static hypergraph.

Experimental setup

Datasets: MIMIC-III Food Recipe (epirecipes) MovieLens

Benchmarks: MIMIC-III Food Recipe MovieLens

Metrics: AUC AUPRC BCE Brier score ARI NMI Micro-F1 Macro-F1 normalized Frobenius error

Baselines: NeuMF AllSet HypeBoy MultiVAE LightGCN EHGNN NNMF GraphSAGE Hyper-SAGNN HRL-Fixed

Builds on: fixed effects / random effects models variational EM score-based SDE denoising score matching

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