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

Abstract

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 $n^{\epsilon }$ 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.

143 pages

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Cited by in corpus (1)

• Sum-of-Squares Lower Bounds for Sparse Independent Set