SQ Lower Bounds for Non-Gaussian Component Analysis with Weaker Assumptions

arXiv:2403.04744v1 Announce Type: new
Abstract: We study the complexity of Non-Gaussian Component Analysis (NGCA) in the Statistical Query (SQ) model. Prior work developed a general methodology to prove SQ lower bounds for this task that have been applicable to a wide range of contexts. In particular, it was known that for any univariate distribution $A$ satisfying certain conditions, distinguishing between a standard multivariate Gaussian and a distribution that behaves like $A$ in a random hidden direction and like a standard …

abstract analysis arxiv assumptions complexity cs.ds cs.lg general math.st methodology prior prove query statistical stat.ml stat.th study type work