# List-Decodable Subspace Recovery via Sum-of-Squares

@article{Bakshi2020ListDecodableSR, title={List-Decodable Subspace Recovery via Sum-of-Squares}, author={Ainesh Bakshi and Pravesh Kothari}, journal={ArXiv}, year={2020}, volume={abs/2002.05139} }

We give the first efficient algorithm for the problem of list-decodable subspace recovery. Our algorithm takes input $n$ samples $\alpha n$ ($\alpha\ll 1/2$) are generated i.i.d. from Gaussian distribution $\mathcal{N}(0,\Sigma_*)$ on $\mathbb{R}^d$ with covariance $\Sigma_*$ of rank $r$ and the rest are arbitrary, potentially adversarial outliers. It outputs a list of $O(1/\alpha)$ projection matrices guaranteed to contain a projection matrix $\Pi$ such that $\|\Pi-\Pi_*\|_F^2 = \kappa^4 \log… CONTINUE READING

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