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literature note /unread FOS Computer and information sciences FOS Mathematics Machine Learning (cs.LG) Machine Learning (stat.ML) Statistics Theory (math.ST)	Note de lecture de *Bridging Maximum Likelihood and Optimal Transport for Efficient Inference and Model Selection in Stochastic Block Models* de Simon Queric, Cédric Vincent-Cuaz, Charles Bouveyron, Marco Corneli.	../these_ref.bib

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FirstAuthor:: Queric, Simon
Author:: Vincent-Cuaz, Cédric
Author:: Bouveyron, Charles
Author:: Corneli, Marco

Title:: Bridging Maximum Likelihood and Optimal Transport for Efficient Inference and Model Selection in Stochastic Block Models

Year:: 2026

Citekey:: quericBridgingMaximumLikelihood2026

itemType:: preprint

DOI:: 10.48550/ARXIV.2605.28488
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We study inference in stochastic block models (SBMs) through the lens of optimal transport (OT). We first establish that maximum likelihood variational inference (MLVI) can be interpreted as a semi-relaxed Gromov-Wasserstein (srGW) projection with entropic regularization. While this formulation yields accurate clustering, the entropic regularization prevents transport plans to be sparse, hindering intrinsic model selection. Consequently, we investigate unregularized srGW estimators, and prove that they consistently recover both the SBM connectivity matrix and latent cluster assignments in the asymptotic regime. However, this asymptotic property does not translate into reliable model selection in finite samples, and calls for additional mechanisms to promote sparsity in the inferred cluster proportions. We empirically show that such a regularized formulation yields estimators that simultaneously recover model parameters and select the number of clusters in a single optimization problem, thereby avoiding costly grid search or heuristic model selection procedures.

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