Graphon Cross-Validation

Wenxuan Zhong
University of Georgia
Tuesday 2nd July 2024
B.5.3, Edificio 14, Politecnico di Milano
Accurate estimation of graphon models plays a crucial role in elucidating connection probabilities among network nodes. However, overfitting poses a significant challenge to the generalizability of these models across various datasets and contexts. The proper calibration of parameters governing the smoothness of graphon functions is essential, yet selecting the most suitable approach remains a pressing issue. In this talk, I will introduce a novel graphon validation method aimed at addressing the limitations of existing approaches, thereby enhancing practical implementation and theoretical comprehension. By conducting extensive simulations and real-world experiments, I showcase the superior computational efficiency and accuracy of our proposed method. Our results demonstrate that the optimal model identified through our approach tends to converge asymptotically to the ideal model determined by the Kullback-Leibler divergence between true and estimated probability matrices. This theoretical insight underscores the enhanced applicability of our method for network analysis in diverse settings. The visit of Prof Wenxuan Zhong is part of the activities of the PRIN research project CoEnv - Complex Environmental Data and Modeling, funded by the Italian Ministry for University and Research and by the NextGenerationEU programme of the European Union.