Tensor cumulants for statistical inference on invariant distributions

arXiv:2404.18735v1 Announce Type: cross
Abstract: Many problems in high-dimensional statistics appear to have a statistical-computational gap: a range of values of the signal-to-noise ratio where inference is information-theoretically possible, but (conjecturally) computationally intractable. A canonical such problem is Tensor PCA, where we observe a tensor $Y$ consisting of a rank-one signal plus Gaussian noise. Multiple lines of work suggest that Tensor PCA becomes computationally hard at a critical value of the signal's magnitude. In particular, below this transition, no low-degree …

abstract arxiv canonical computational cs.cc cs.ds gap inference information math.pr math.st noise observe pca signal statistical statistics stat.ml stat.th tensor type values