Nonparametric estimation of time-varying network connections by multi-stage smoothing

2026-05-07

AI Summary

This study addresses the nonparametric estimation of time-varying edge connection probabilities in latent networks from multi-temporal observational data. To this end, the authors propose a multi-stage smoothing framework: first applying local temporal smoothing to each edge, then performing node-wise smoothing based on a data-driven neighborhood construction, and optionally incorporating global temporal smoothing to enhance temporal consistency. The method leverages both the temporal Hölder smoothness of graphon functions and the piecewise Lipschitz structure of latent variables, yielding theoretically guaranteed estimation accuracy. Extensive simulations and real-data analyses demonstrate that the proposed approach effectively captures both the smooth evolution and structural patterns of network connectivity, outperforming existing methods in estimation performance.

Abstract

We consider the problem of estimating the underlying edge probabilities of a time-varying network observed at multiple time points. The probability structure is represented by a time-varying graphon that satisfies temporal Hölder smoothness and piecewise Lipschitz conditions in the latent variables. We propose a multi-stage smoothing estimator that first applies temporal local smoothing to each edge and then performs node-domain smoothing using a data-driven neighborhood construction adapted from the method. An additional temporal smoothing step is introduced as an optional refinement when uniform accuracy over the entire time domain is required. Simulation studies demonstrate the benefits of combining temporal and node-domain smoothing under different generative models. We also apply the method to a real time-varying network dataset and show that it captures both smooth temporal evolution and structural patterns in the connectivity.

Problem

• time-varying network
• edge probability estimation
• graphon
• nonparametric estimation
• temporal smoothing

Innovation

• multi-stage smoothing
• time-varying graphon
• nonparametric estimation
• temporal Hölder smoothness
• data-driven neighborhood