44 citations · 142 across the 15 of their papers we have counts for
7 papers · 1 filter
Deep learning: a statistical viewpoint
Peter L. Bartlett, Andrea Montanari, Alexander Rakhlin
The remarkable practical success of deep learning has revealed some major surprises from a theoretical perspective. In particular, simple gradient methods easily find near-optimal…
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,…
On the Multiple Descent of Minimum-Norm Interpolants and Restricted Lower Isometry of Kernels
Tengyuan Liang, Alexander Rakhlin, Xiyu Zhai
We study the risk of minimum-norm interpolants of data in Reproducing Kernel Hilbert Spaces. Our upper bounds on the risk are of a multiple-descent shape for the various scalings o…
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…
Just Interpolate: Kernel "Ridgeless" Regression Can Generalize
Tengyuan Liang, Alexander Rakhlin
In the absence of explicit regularization, Kernel "Ridgeless" Regression with nonlinear kernels has the potential to fit the training data perfectly. It has been observed empirical…