# Lattice-Based Methods Surpass Sum-of-Squares in Clustering

@article{Zadik2021LatticeBasedMS, title={Lattice-Based Methods Surpass Sum-of-Squares in Clustering}, author={Ilias Zadik and Min Jae Song and Alexander S. Wein and Joan Bruna}, journal={ArXiv}, year={2021}, volume={abs/2112.03898} }

Clustering is a fundamental primitive in unsupervised learning which gives rise to a rich class of computationally-challenging inference tasks. In this work, we focus on the canonical task of clustering d-dimensional Gaussian mixtures with unknown (and possibly degenerate) covariance. Recent works (Ghosh et al. ’20; Mao, Wein ’21; Davis, Diaz, Wang ’21) have established lower bounds against the class of low-degree polynomial methods and the sum-of-squares (SoS) hierarchy for recovering certain…

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