Network Model Averaging Prediction for Latent Space Models by K-fold Edge Cross-Validation
Yan Zhang, Jun Liao, Xinyan Fan, Kuangnan Fang, Yuhong Yang · Statistica Sinica · 2026
In complex systems, networks describe relationships between nodes through edges.Latent space models are widely used for network tasks such as community detection and link prediction due to their interpretability and visualization power.However, when the network size is small or the true latent dimension is large, a single latent space model may suffer from high estimation error or model misspecification.To address this, we propose Network Model Averaging (NetMA), which combines multiple latent space models with different dimensions.The weights are estimated using a K-fold edge cross-validation scheme that is specially designed for network data.Our method applies to both singlelayer and multi-layer networks.We provide theoretical guarantees for NetMA.When all candidate models are misspecified, NetMA still achieves asymptotically optimal prediction.When models with large enough latent dimensions are included, NetMA assigns nearly all weights to them.We also prove that the estimated weights converge to the optimal weights.Simulation studies show that NetMA performs better than model selection and simple averaging.It even outperforms the "oracle" model when the true latent dimension is large.Applications to mutual-following and virtual event networks further highlight the strong performance of NetMA in link prediction.