Network Cross-Validation for Nested Models by Edge-Sampling

TL;DR

This paper introduces a penalized edge-sampling cross-validation method for nested network model selection, providing theoretical guarantees and demonstrating improved stability and accuracy in empirical tests.

Contribution

It proposes a novel cross-validation framework with complexity penalties for network models, offering the first consistency guarantees across multiple model classes.

Findings

Method achieves stable, accurate model selection in simulations.

Provides the first consistency guarantees for cross-model selection.

Demonstrates effectiveness on real network data.

Abstract

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, there remains a lack of systematic theoretical understanding for this problem when comparing across different model classes. In this paper, to address this challenging problem, 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 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.