# Penalized Network Cross-Validation for Nested Models by Edge-Sampling

arXiv: https://arxiv.org/abs/2506.14244 · HTML: https://mlsanity.com/paper/2506.14244/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 17 Jun 2025.

## Built on by (most cited first, 1 of 1)

- [Nonparametric estimation of time-varying network connections by multi-stage smoothing](https://mlsanity.com/paper/2605.06862/) (2026)

## Abstract (arXiv)

In the network literature, a wide range of statistical models has been proposed to exploit structural patterns in the data. Therefore, model selection between different models is a fundamental problem. However, systematic theoretical understanding remains limited when comparisons involve different model classes. To address this challenging issue, we propose a penalized edge-sampling cross-validation framework for nested network model selection. By incorporating a model complexity penalty into the evaluation process, our method effectively mitigates the overfitting tendency of cross-validation and adapts to varying model structures. This framework supports comparisons among widely used models, including stochastic block models (SBMs), degree-corrected SBMs (DCBMs), and graphon models, providing the first consistency guarantees for model selection across these settings to the best of our knowledge. Empirical evaluations, including both simulated data and the ``Political Books'' network, demonstrate that our method yields stable and accurate performance across various scenarios.