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

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]

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