Gradient EM algorithm achieves global convergence for over-parameterized Gaussian Mixtures

Researchers have established a global convergence guarantee for the gradient Expectation-Maximization (EM) algorithm when applied to over-parameterized Gaussian Mixture Models (GMMs). This marks the first such result for EM or its gradient variant beyond the specific case of two components. The study demonstrates that with mild over-parameterization, where the learning model uses $n = \Omega(m\log m)$ components to fit an $m$-component ground truth GMM, randomly initialized gradient EM can converge to the correct solution within polynomial time and sample complexity. The analysis introduces novel tools for GMM analysis to characterize the algorithm's dynamics and the likelihood loss landscape. AI

IMPACT Provides theoretical guarantees for a fundamental statistical learning algorithm, potentially improving the reliability of GMM fitting in various ML applications.

RANK_REASON Academic paper detailing a theoretical advance in machine learning algorithms. [lever_c_demoted from research: ic=1 ai=1.0]

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• arXiv
• expectation–maximization algorithm
• Gaussian Mixture Models
• machine learning
• Mo Zhou
• statistics

• paper
• model release
• other

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