Machinery for Proving Sum-of-Squares Lower Bounds on Certification Problems
Aaron Henry Potechin, Goutham Rajendran · arXiv (Cornell University) · 2020
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.