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.

翻译：在本文中，我们通过推广Barak等人[FOCS 2016]用于证明种植团问题平方和下界的技巧，构建了证明认证问题平方和下界的通用机制。利用这一机制，我们证明了张量PCA、稀疏PCA的Wishart模型以及一种我们称之为“种植稍密子图”的种植团变体在$n^{\epsilon}$次平方和下的下界。