Network Perturbation Aggregation for Graphon Estimation

Da Wang, Jun S. Liu, Yongkai Chen, Yuyao Wang, Huimin Cheng

Abstract: In recent years, various methods have been proposed to estimate the edge probability under the graphon model given a single observed network. Since the presence or absence of edges in the observed network is a stochastic realization from the underlying probability structure, estimating edge probabilities based on only a single observed realization is inherently limited and leads to estimates with high variance and high mean squared error (MSE). To address this issue, we propose the Network Perturbation aggregating (Net-Paging) method. The key idea is to construct multiple perturbed networks that preserve key graphon properties, mimicking multiple replications. We then obtain graphon estimates from each perturbed network and average these estimates to obtain the final estimate. We theoretically show that the more perturbed samples used in our algorithm, the smaller the MSE, with a linear dependency. Extensive simulation experiments and real data analysis show that Net-Paging effectively reduces the variance and MSE compared to existing methods.

Submission Type: Research Article

Code: https://github.com/wd5457/Net-Paging

Submission Number: 10