# Overspecified Mixture Discriminant Analysis: Exponential Convergence, Statistical Guarantees, and Remote Sensing Applications

arXiv: https://arxiv.org/abs/2510.27056 · HTML: https://mlsanity.com/paper/2510.27056/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 10 of its 31 references that are in the map.
- First posted on arXiv 30 Oct 2025.

## Builds on (most cited first, 10 of 10)

- [EuroSAT: A Novel Dataset and Deep Learning Benchmark for Land Use and Land Cover Classification](https://mlsanity.com/paper/1709.00029/) (2017)
- [Statistical guarantees for the EM algorithm: From population to sample-based analysis](https://mlsanity.com/paper/1408.2156/) (2014)
- [Ten Steps of EM Suffice for Mixtures of Two Gaussians](https://mlsanity.com/paper/1609.00368/) (2016)
- [Singularity, Misspecification, and the Convergence Rate of EM](https://mlsanity.com/paper/1810.00828/) (2018)
- [Sharp Analysis of Expectation-Maximization for Weakly Identifiable Models](https://mlsanity.com/paper/1902.00194/) (2019)
- [A Two-round Variant of EM for Gaussian Mixtures](https://mlsanity.com/paper/1301.3850/) (2013)
- [Improved Convergence Guarantees for Learning Gaussian Mixture Models by EM and Gradient EM](https://mlsanity.com/paper/2101.00575/) (2021)
- [Local Minima Structures in Gaussian Mixture Models](https://mlsanity.com/paper/2009.13040/) (2020)
- [Statistical Guarantees for Estimating the Centers of a Two-component Gaussian Mixture by EM](https://mlsanity.com/paper/1608.02280/) (2016)
- [Toward Global Convergence of Gradient EM for Over-Parameterized Gaussian Mixture Models](https://mlsanity.com/paper/2407.00490/) (2024)

## Abstract (arXiv)

This study explores the classification error of Mixture Discriminant Analysis (MDA) in scenarios where the number of mixture components exceeds those present in the actual data distribution, a condition known as overspecification. We use a two-component Gaussian mixture model within each class to fit data generated from a single Gaussian, analyzing both the algorithmic convergence of the Expectation-Maximization (EM) algorithm and the statistical classification error. We demonstrate that, with suitable initialization, the EM algorithm converges exponentially fast to the Bayes risk at the population level. Further, we extend our results to finite samples, showing that the classification error converges to Bayes risk with a rate n-1/2 under mild conditions on the initial parameter estimates and sample size. This work provides a rigorous theoretical framework for understanding the performance of overspecified MDA, which is often used empirically in complex data settings, such as image and text classification. To validate our theory, we conduct experiments on remote sensing datasets.