# The More, the Merrier: the Blessing of Dimensionality for Learning Large Gaussian Mixtures

@article{Anderson2014TheMT, title={The More, the Merrier: the Blessing of Dimensionality for Learning Large Gaussian Mixtures}, author={J. Anderson and Mikhail Belkin and Navin Goyal and Luis Rademacher and James R. Voss}, journal={ArXiv}, year={2014}, volume={abs/1311.2891} }

In this paper we show that very large mixtures of Gaussians are efficiently learnable in high dimension. More precisely, we prove that a mixture with known identical covariance matrices whose number of components is a polynomial of any fixed degree in the dimension n is polynomially learnable as long as a certain non-degeneracy condition on the means is satisfied. It turns out that this condition is generic in the sense of smoothed complexity, as soon as the dimensionality of the space is high… Expand

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