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 that …

The least squares estimator (LSE) is shown to be suboptimal in squared error loss in the
usual nonparametric regression model with Gaussian errors for $ d\geq 5$ for each of the …

Suboptimality of constrained least squares and improvements via non-linear predictors Page 1
Bernoulli 29(1), 2023, 473–495 https://doi.org/10.3150/22-BEJ1465 Suboptimality of …

We study the minimal squared error of the Empirical Risk Minimization (ERM) procedure in
the task of regression, both in random and fixed design settings. Our sharp lower bounds …

Convex regression is the problem of fitting a convex function to a data set consisting of input-
output pairs. We present a new approach to this problem called spectrahedral regression, in …

This paper, inspired by a collaboration with a leading consumer electronics retailer in the
Middle East, explores the challenge of demand learning and pricing using separable …

Variational regularization is a classical technique to solve statistical inference tasks and
inverse problems, with modern data-driven approaches parameterizing regularizers via …

This dissertation investigates non-parametric regression over large function classes,
specifically, non-Donsker classes. We will present the concept of non-Donsker classes and …

In this paper, we consider nonparametric estimation over general Dirichlet metric measure
spaces. Unlike the more commonly studied reproducing kernel Hilbert space, whose …

We consider estimating a compact set from finite data by approximating the support function
of that set via sublinear regression. Support functions uniquely characterize a compact set …