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What are the current best results on fitting mixtures of Gaussians with any algorithm (EM or something fancier)? Specifically, if I know only the number of components, what are the sharpest sample complexity bounds for recovering the mixture weights, the means, and the covariances?

I'm looking for an entry into the literature, so if there are particularly well-written and relative up-to-date papers that have a strong pedagogical / survey aspect to them, I'd appreciate pointers in those directions too.

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