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Gradient EM needs $\sqrt{d}$ separation for Gaussian mixtures in high dimensions

By PulseAugur Editorial · [2 sources] ·

A new paper explores the necessity of component separation for gradient EM algorithms to learn Gaussian mixture models in high dimensions. The research demonstrates that a separation of order $\Omega(d^{0.5-\epsilon})$ is insufficient for guaranteed global convergence in sub-exponential time, even in over-parameterized settings. This finding establishes an almost optimal worst-case lower bound for the required ground-truth component separation. AI

IMPACT Establishes a theoretical lower bound for learning Gaussian mixtures, impacting algorithm design and analysis in high-dimensional settings.

RANK_REASON The cluster contains a single academic paper detailing theoretical findings in machine learning. [lever_c_demoted from research: ic=1 ai=1.0]

Read on Hugging Face Daily Papers →

AI-generated summary · Google Gemini · from 2 sources. How we write summaries →

Gradient EM needs $\sqrt{d}$ separation for Gaussian mixtures in high dimensions

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The cluster contains a single academic paper detailing theoretical findings in machine learning. [lever_c_demoted from research: ic=1 ai=1.0]
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COVERAGE [2]

  1. arXiv cs.LG TIER_1 English(EN) · Yiran Zhang, Mo Zhou, Weihang Xu, Maryam Fazel, Simon S. Du ·

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

    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…

  2. Hugging Face Daily Papers TIER_1 English(EN) ·

    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-parameteriz…

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