English(EN) Is $\sqrt{d}$ Separation Necessary for Gradient EM to Learn Gaussian Mixtures in High Dimensions?

梯度EM在高维高斯混合模型中学习需要 $\sqrt{d}$ 分离

作者 PulseAugur 编辑部 · [1 个来源] · 2026-10-07 04:00

一篇新论文探讨了梯度EM算法在高维空间中学习高斯混合模型时，分量分离的必要性。研究表明，即使在过参数化的情况下，$\\Omega(d^{0.5-\epsilon})$ 阶的分离也不足以保证在亚指数时间内全局收敛。这一发现为所需真实分量分离设定了一个近乎最优的最坏情况下界。 AI

影响为学习高斯混合模型建立了理论下界，影响高维设置下的算法设计和分析。

排序理由该集群包含一篇详细介绍机器学习理论发现的学术论文。[lever_c_demoted from research: ic=1 ai=1.0]

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$梯度EM在高维高斯混合模型中学习需要 $\sqrt{d}$ 分离$

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arXiv cs.LG TIER_1 English(EN) · Yiran Zhang, Mo Zhou, Weihang Xu, Maryam Fazel, Simon S. Du · 2026-10-07 04:00

高维情况下，梯度EM算法学习高斯混合模型是否需要$\sqrt{d}$分离？

arXiv:2610.07551v1 Announce Type: cross Abstract: 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 l…