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 · [2 个来源] · 2026-10-06 00:29

一篇新论文探讨了梯度EM算法在高维高斯混合模型学习中对分量分离的必要性。研究表明，即使在过参数化的情况下，阶数约为 $\Omega(d^{0.5-\epsilon})$ 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度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]

AI 生成摘要 · Google Gemini · 来自 2 个来源。我们如何撰写摘要 →

$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…
Hugging Face Daily Papers TIER_1 English(EN) · 2026-10-06 00:29

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？

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-parameteriz…