Transcendental Regularization of Finite Mixtures:Theoretical Guarantees and Practical Limitations

• URL: http://arxiv.org/abs/2602.03889v1
• Date: Tue, 03 Feb 2026 05:12:14 GMT
• Title: Transcendental Regularization of Finite Mixtures:Theoretical Guarantees and Practical Limitations
• Authors: Ernest Fokoué,
• Abstract summary: We introduce transcendental regularization, a penalized likelihood framework with analytic barrier functions that prevent degeneracy while maintaining efficiency.<n>Our work provides both a novel theoretical framework and an honest assessment of practical limitations, implemented in an open-source R package.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Finite mixture models are widely used for unsupervised learning, but maximum likelihood estimation via EM suffers from degeneracy as components collapse. We introduce transcendental regularization, a penalized likelihood framework with analytic barrier functions that prevent degeneracy while maintaining asymptotic efficiency. The resulting Transcendental Algorithm for Mixtures of Distributions (TAMD) offers strong theoretical guarantees: identifiability, consistency, and robustness. Empirically, TAMD successfully stabilizes estimation and prevents collapse, yet achieves only modest improvements in classification accuracy-highlighting fundamental limits of mixture models for unsupervised learning in high dimensions. Our work provides both a novel theoretical framework and an honest assessment of practical limitations, implemented in an open-source R package.

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