Anindya De, Elchanan Mossel, Joe Neeman

A natural problem in high-dimensional inference is to decide if a classifier $f:\mathbb{R}^n \rightarrow \{-1,1\}$ depends on a small number of linear directions of its input data. Call a function $g: \mathbb{R}^n \rightarrow \{-1,1\}$, a linear $k$-junta if it is completely determined by some $k$-dimensional subspace of the input space. ... more >>>