Work

Normalized Likelihood Criteria for Model Selection in the Stochastic Block Model

Year: 2026

Type: preprint

Abstract: Estimating the number of communities is a fundamental problem in network analysis under the stochastic block model (SBM). In this paper, we study penalized estimators for this task based on normalized likelihood criteria. We show that a penalized estimator derived from the Normalized Maximum Likelihood (NML) is strongly consistent with a logarithmic penalty term, although its computation is intractable. To overcome this limitation, we consider the Normalized Maximum Complete Likelihood (NMCL) and the Decomposed Normalized Maximum Likelihood (DNML). The DNML admits an explicit formulation with cubic computational complexity in the number of nodes. We prove that the NMCL- and DNML- based estimators are strongly consistent for sparse networks in which the average node degree diverges with the network size. Empirical results show that the DNML estimator performs competitively with existing methods, particularly in unbalanced networks.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2604.10205

Authors: Cerqueira, Andressa, Baptistão, Felipe

Institution: Universidade Federal de São Carlos

Topic: Complex Network Analysis Techniques

Subfield: Statistical and Nonlinear Physics

Field: Physics and Astronomy

Domain: Physical Sciences

Open Access status: green

Funders: Fundação de Amparo à Pesquisa do Estado de São Paulo, Conselho Nacional de Desenvolvimento Científico e Tecnológico

Awards: Stochastic systems modeling, Statistical Analysis of Complex Networks, G979006760

OpenAlex ID: W7154389558

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