Machinery for Proving Sum-of-Squares Lower Bounds on Certification Problems

11/09/2020

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by   Aaron Potechin, et al.

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In this paper, we construct general machinery for proving Sum-of-Squares lower bounds on certification problems by generalizing the techniques used by Barak et al. [FOCS 2016] to prove Sum-of-Squares lower bounds for planted clique. Using this machinery, we prove degree n^ϵ Sum-of-Squares lower bounds for tensor PCA, the Wishart model of sparse PCA, and a variant of planted clique which we call planted slightly denser subgraph.