3 papers
math.ST2025
An Efficient Minimax Optimal Estimator For Multivariate Convex Regression
Gil Kur, Eli Putterman
This work studies the computational aspects of multivariate convex regression in dimensions . Our results include the \emph{first} estimators that are minimax optimal (up…
math.MG2025
On the Optimality of Random Partial Sphere Coverings in High Dimensions
Steven Hoehner, Gil Kur
Given geodesic caps on the unit sphere in , whose total normalized surface area is one, what is the maximal proportion of the sphere that their union can cover? I…
math.ST2025
On the Variance, Admissibility, and Stability of Empirical Risk Minimization
Gil Kur, Eli Putterman, Alexander Rakhlin
It is well known that Empirical Risk Minimization (ERM) may attain minimax suboptimal rates in terms of the mean squared error (Birgé and Massart, 1993). In this paper, we prove t…