This paper addresses the problem of testing whether a Boolean-valued function f is a halfspace, i.e. a function of the form f(x) = sgn(w·x−θ). We consider halfspaces over the ...
Kevin Matulef, Ryan O'Donnell, Ronitt Rubinfeld, R...
— We prove the following strong hardness result for learning: Given a distribution on labeled examples from the hypercube such that there exists a monomial (or conjunction) consi...
The computation of the Tukey depth, also called halfspace depth, is very demanding, even in low dimensional spaces, because it requires that all possible one-dimensional projectio...
We prove the existence of an algorithm A for computing 2-d or 3-d convex hulls that is optimal for every point set in the following sense: for every set S of n points and for ever...