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Characterizing Heterogeneous Rates in Finite Mixture Estimation via Partial Optimal Transport

arXiv · AI, language, vision and robotics · article · Sep 15, 2026 · UTC

Parameter estimation in finite mixture models can exhibit highly heterogeneous convergence behavior: locally isolated components may be estimated substantially faster than groups of competing components. Existing analyses based on Wasserstein distances typically characterize only the worst-case rate and therefore do not fully capture this local heterogeneity. In this paper, we introduce a Voronoi-based partial optimal transport (VPOT) framework for obtaining refined local and global convergence guarantees for the maximum likelihood estimator of the mixing measure. The key geometric idea is to

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