Is $\sqrt{d}$ Separation Necessary for Gradient EM to Learn Gaussian Mixtures in High Dimensions?
Learning Gaussian mixture models (GMMs) using the Expectation-Maximization (EM) algorithm and its gradient-based variants is a fundamental problem in machine learning. It is known that randomly initialized (gradient) EM fails to learn multi-component GMMs in the exact-parameterized setting, where the number of components matches that of the ground-truth GMM. Recently, global convergence of gradient EM has been established in the over-parameterized setting, where more components are used, provided that the ground-truth components are well separated. In particular, the minimum separation between ground-truth components is required to scale as $Ω(\sqrt{d})$, where $d$ is the dimension. In th...
| Authors | Yiran Zhang, Mo Zhou, Weihang Xu et al. |
|---|---|
| Primary category | stat.ML |
| Published | 6 October 2026 |
| Last updated at source | 6 October 2026 |
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