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Learning Latent Structures in Network Games via Data-Dependent Gated-Prior Graph Variational Autoencoders

ICML 2024 · Graph learning › Graph self-supervised learning · approach: Diffusion-based graph generation

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Proposes GPGVAE, an unsupervised graph VAE with a data-dependent gated (correlation/anticorrelation) prior that infers latent interaction type and network structure from equilibrium actions in network games.

Problem

Inferring latent network structures and interaction types (strategic complement vs. substitute) among individuals from their observed actions in network games, without knowing utility functions or partial network connections.

Approach

A data-dependent gated prior that switches between correlation and anticorrelation edge priors computed from game actions, gated by a latent interaction type predicted by a spectral GNN encoder pretrained on synthetic games, combined with a Transformer-based mixture-of-Bernoulli structure encoder and GNN decoder trained stage-wise with Monte Carlo gradients.

Key results

• On Indian Villages, GPGVAE reaches 56.77 AUC, slightly below Graphical Lasso (56.91), the only dataset where it is not best.
• GPGVAE achieves 75.35 AUC on Foursquare New York ratings versus 73.62 for LinQuadOpt and improves LA ratings by about 6.78% over the best baseline.
• On BH graphical games with BA graphs GPGVAE gets 68.02 AUC, versus 67.57 for Graphical Lasso.

Measured effects reported in the paper

Surprising findings

• No single prior (correlation or anticorrelation) dominates across all game settings, motivating the gated mixture prior.
• Gradient estimator choice (pathwise, score function, measure-valued) made little difference in AUC in the ablation.

Limitations

• Assumes observed actions satisfy Nash equilibrium, which may be violated in practice.
• Pretraining of the interaction encoder requires synthetic data since real-world interaction types are unlabeled.
• Performance on Indian Villages is limited by having only 10 games per graph.

Experimental setup

Datasets: Indian Villages Foursquare (New York, Sao Paulo) Yelp (PA, LA) Synthetic BA/ER/WS network games

Benchmarks: Synthetic linear quadratic, linear influence, BH graphical games Indian Villages Foursquare Yelp

Metrics: AUC

Baselines: Graphical Lasso Regularized Lasso LinQuadOpt BlockRegression VGAE VGCN DAG-GNN uGLAD LDS NodeFormer

Builds on: Graph VAE (VGAE) graphical lasso linear quadratic games Gumbel-Softmax REINFORCE

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