Contrastive Moments: Unsupervised Halfspace Learning in Polynomial Time. (arXiv:2311.01435v1 [cs.LG])

We give a polynomial-time algorithm for learning high-dimensional halfspaces
with margins in $d$-dimensional space to within desired TV distance when the
ambient distribution is an unknown affine transformation of the $d$-fold
product of an (unknown) symmetric one-dimensional logconcave distribution, and
the halfspace is introduced by deleting at least an $\epsilon$ fraction of the
data in one of the component distributions. Notably, our algorithm does not
need labels and establishes the unique (and efficient) identifiability of the
hidden halfspace under this …

algorithm ambient arxiv distribution least margins moments polynomial product space transformation unsupervised