Showing math.STShow all
3 papers · 1 filter
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.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…
math.ST2024
Convex Regression in Multidimensions: Suboptimality of Least Squares Estimators
Gil Kur, Fuchang Gao, Adityanand Guntuboyina +1
Under the usual nonparametric regression model with Gaussian errors, Least Squares Estimators (LSEs) over natural subclasses of convex functions are shown to be suboptimal for esti…