# Transcendental Regularization of Finite Mixtures:Theoretical Guarantees and Practical Limitations

arXiv: https://arxiv.org/abs/2602.03889 · HTML: https://mlsanity.com/paper/2602.03889/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 1 of its 19 references that are in the map.
- First posted on arXiv 3 Feb 2026.

## Builds on (most cited first, 1 of 1)

- [Variational Inference: A Review for Statisticians](https://mlsanity.com/paper/1601.00670/) (2016)

## Abstract (arXiv)

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.