18 citations · 73 across the 13 of their papers we have counts for
7 papers · 1 filter
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 th…
Tyler's and Maronna's M-estimators: Non-Asymptotic Concentration Results
Elad Romanov, Gil Kur, Boaz Nadler
Tyler's and Maronna's M-estimators, as well as their regularized variants, are popular robust methods to estimate the scatter or covariance matrix of a multivariate distribution. I…
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…
On the Minimal Error of Empirical Risk Minimization
Gil Kur, Alexander Rakhlin
We study the minimal error of the Empirical Risk Minimization (ERM) procedure in the task of regression, both in the random and the fixed design settings. Our sharp lower bounds sh…
On Suboptimality of Least Squares with Application to Estimation of Convex Bodies
Gil Kur, Alexander Rakhlin, Adityanand Guntuboyina
We develop a technique for establishing lower bounds on the sample complexity of Least Squares (or, Empirical Risk Minimization) for large classes of functions. As an application,…
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…
Optimality of Maximum Likelihood for Log-Concave Density Estimation and Bounded Convex Regression
Gil Kur, Yuval Dagan, Alexander Rakhlin
In this paper, we study two problems: (1) estimation of a -dimensional log-concave distribution and (2) bounded multivariate convex regression with random design with an underly…