Paper
Maximum entropy based testing in network models: ERGMs and constrained optimization
Authors
Subhrosekhar Ghosh, Rathindra Nath Karmakar, Samriddha Lahiry
Abstract
Stochastic network models play a central role across a wide range of scientific disciplines, and questions of statistical inference arise naturally in this context. In this paper we investigate goodness-of-fit and two-sample testing procedures for statistical networks based on the principle of maximum entropy (MaxEnt). Our approach formulates a constrained entropy-maximization problem on the space of networks, subject to prescribed structural constraints. The resulting test statistics are defined through the Lagrange multipliers associated with the constrained optimization problem, which, to our knowledge, is novel in the statistical networks literature. We establish consistency in the classical regime where the number of vertices is fixed. We then consider asymptotic regimes in which the graph size grows with the sample size, developing tests for both dense and sparse settings. In the dense case, we analyze exponential random graph models (ERGM) (including the Erdös-Rènyi models), while in the sparse regime our theory applies to Erd{ö}s-R{è}nyi graphs. Our analysis leverages recent advances in nonlinear large deviation theory for random graphs. We further show that the proposed Lagrange-multiplier framework connects naturally to classical score tests for constrained maximum likelihood estimation. The results provide a unified entropy-based framework for network model assessment across diverse growth regimes.
Metadata
Related papers
Fractal universe and quantum gravity made simple
Fabio Briscese, Gianluca Calcagni • 2026-03-25
POLY-SIM: Polyglot Speaker Identification with Missing Modality Grand Challenge 2026 Evaluation Plan
Marta Moscati, Muhammad Saad Saeed, Marina Zanoni, Mubashir Noman, Rohan Kuma... • 2026-03-25
LensWalk: Agentic Video Understanding by Planning How You See in Videos
Keliang Li, Yansong Li, Hongze Shen, Mengdi Liu, Hong Chang, Shiguang Shan • 2026-03-25
Orientation Reconstruction of Proteins using Coulomb Explosions
Tomas André, Alfredo Bellisario, Nicusor Timneanu, Carl Caleman • 2026-03-25
The role of spatial context and multitask learning in the detection of organic and conventional farming systems based on Sentinel-2 time series
Jan Hemmerling, Marcel Schwieder, Philippe Rufin, Leon-Friedrich Thomas, Mire... • 2026-03-25
Raw Data (Debug)
{
"raw_xml": "<entry>\n <id>http://arxiv.org/abs/2602.20844v1</id>\n <title>Maximum entropy based testing in network models: ERGMs and constrained optimization</title>\n <updated>2026-02-24T12:35:08Z</updated>\n <link href='https://arxiv.org/abs/2602.20844v1' rel='alternate' type='text/html'/>\n <link href='https://arxiv.org/pdf/2602.20844v1' rel='related' title='pdf' type='application/pdf'/>\n <summary>Stochastic network models play a central role across a wide range of scientific disciplines, and questions of statistical inference arise naturally in this context. In this paper we investigate goodness-of-fit and two-sample testing procedures for statistical networks based on the principle of maximum entropy (MaxEnt). Our approach formulates a constrained entropy-maximization problem on the space of networks, subject to prescribed structural constraints. The resulting test statistics are defined through the Lagrange multipliers associated with the constrained optimization problem, which, to our knowledge, is novel in the statistical networks literature.\n We establish consistency in the classical regime where the number of vertices is fixed. We then consider asymptotic regimes in which the graph size grows with the sample size, developing tests for both dense and sparse settings. In the dense case, we analyze exponential random graph models (ERGM) (including the Erdös-Rènyi models), while in the sparse regime our theory applies to Erd{ö}s-R{è}nyi graphs.\n Our analysis leverages recent advances in nonlinear large deviation theory for random graphs. We further show that the proposed Lagrange-multiplier framework connects naturally to classical score tests for constrained maximum likelihood estimation. The results provide a unified entropy-based framework for network model assessment across diverse growth regimes.</summary>\n <category scheme='http://arxiv.org/schemas/atom' term='math.ST'/>\n <category scheme='http://arxiv.org/schemas/atom' term='cs.IT'/>\n <category scheme='http://arxiv.org/schemas/atom' term='math.PR'/>\n <category scheme='http://arxiv.org/schemas/atom' term='stat.ME'/>\n <category scheme='http://arxiv.org/schemas/atom' term='stat.ML'/>\n <published>2026-02-24T12:35:08Z</published>\n <arxiv:primary_category term='math.ST'/>\n <author>\n <name>Subhrosekhar Ghosh</name>\n </author>\n <author>\n <name>Rathindra Nath Karmakar</name>\n </author>\n <author>\n <name>Samriddha Lahiry</name>\n </author>\n </entry>"
}