Universal Inference for model selection on networks

2026-06-29

AI Summary

This work addresses the challenges of model selection and hypothesis testing in network data, where strong dependencies and a single observed sample often render existing methods inadequate due to their lack of finite-sample guarantees and limited applicability. The authors propose a general framework based on Universal Inference, which employs edge sampling to partition the network into two subnetworks with controllable dependence structures. This approach yields the first e-value statistic tailored for dependent data, offering strict Type I error control in finite samples and logarithmic consistency under a broad class of alternative models. Empirical evaluations demonstrate that the method achieves both theoretical rigor and strong practical performance in tasks such as random graph model selection and community number estimation.

Abstract

Model selection and hypothesis testing are important tasks on networks. A key challenge lies in the inherent dependence in network data, as well as the fact that typically only a single realization is observed. As a result, many existing methods must be carefully tailored to specific models and only come with asymptotic theoretical guarantees. In this work, however, we propose a general model selection framework using Universal Inference, making our method widely applicable to various testing scenarios. Since Universal Inference requires two sets of data, we employ edge sampling to obtain proper networks with tractable dependence. We prove that the proposed statistic is an e-value, thus controlling the type I error rate in finite samples under nearly any hypothesis test. To our knowledge, this is the first Universal Inference-type statistic constructed from dependent splits of data as well as the first finite-sample testing guarantee for hypothesis testing on networks. We also prove that the logarithm of the test statistic diverges to positive infinity under various alternative models. On simulated and real-world networks, the proposed method performs well on tasks such as choosing the random graph model and the number of communities.

Problem

• model selection
• hypothesis testing
• network data
• dependence
• finite-sample guarantee

Innovation

• Universal Inference
• network hypothesis testing
• e-value
• edge sampling
• finite-sample guarantee