# Statistical Guarantees for Estimating the Centers of a Two-component Gaussian Mixture by EM

arXiv: https://arxiv.org/abs/1608.02280 · HTML: https://mlsanity.com/paper/1608.02280/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 7 Aug 2016.

## Built on by (most cited first, 8 of 8)

- [The EM Algorithm is Adaptively-Optimal for Unbalanced Symmetric Gaussian Mixtures](https://mlsanity.com/paper/2103.15653/) (2021)
- [Toward Global Convergence of Gradient EM for Over-Parameterized Gaussian Mixture Models](https://mlsanity.com/paper/2407.00490/) (2024)
- [Unveiling the Cycloid Trajectory of EM Iterations in Mixed Linear Regression](https://mlsanity.com/paper/2405.18237/) (2024)
- [Factor Adjusted Spectral Clustering for Mixture Models](https://mlsanity.com/paper/2408.12564/) (2024)
- [Mean Estimation in High-Dimensional Binary Markov Gaussian Mixture Models](https://mlsanity.com/paper/2206.02455/) (2022)
- [Adaptive Mean Estimation in the Hidden Markov sub-Gaussian Mixture Model](https://mlsanity.com/paper/2406.12446/) (2024)
- [Learning Overspecified Gaussian Mixtures Exponentially Fast with the EM Algorithm](https://mlsanity.com/paper/2506.11850/) (2025)
- [Overspecified Mixture Discriminant Analysis: Exponential Convergence, Statistical Guarantees, and Remote Sensing Applications](https://mlsanity.com/paper/2510.27056/) (2025)

## Abstract (arXiv)

Recently, a general method for analyzing the statistical accuracy of the EM algorithm has been developed and applied to some simple latent variable models [Balakrishnan et al. 2016]. In that method, the basin of attraction for valid initialization is required to be a ball around the truth. Using Stein's Lemma, we extend these results in the case of estimating the centers of a two-component Gaussian mixture in d dimensions. In particular, we significantly expand the basin of attraction to be the intersection of a half space and a ball around the origin. If the signal-to-noise ratio is at least a constant multiple of  √dlog d , we show that a random initialization strategy is feasible.