האם פרידה של √d נדרשת ללמידה של מערכות מערכות גאוסיאניות בממדים גבוהים?

תקציר מקורי באנגליתarXiv: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 learn multi-component GMMs in the exact-parameterized setting, where the number of components matches that of the ground-truth GMM. Recently, global convergence of gradient EM has been established in the over-parameterized setting, where more components are used, provided that the ground-truth components are well separated. In particular, the minimum separation between ground-truth components is required to scale as $\Omega(\sqrt{d})$, where $d$ is the dimension. In this paper, we show that this dimensional dependen