Manifold learning (ML), also known as nonlinear dimension reduction, is a set of methods to
find the low-dimensional structure of data. Dimension reduction for large, high-dimensional …

Nonparametric regression using deep neural networks with ReLU activation function Page 1
The Annals of Statistics 2020, Vol. 48, No. 4, 1875–1897 https://doi.org/10.1214/19-AOS1875 …

Weak Convergence Page 1 1.3 Weak Convergence In this section IDl and IE are metric spaces
with metrics d and e, respectively. The set of all continuous, bounded functions f: IDl 1--+ IR is …

Concentration inequalities deal with deviations of functions of independent random
variables from their expectation. In the last decade new tools have been introduced making …

In many areas, practitioners seek to use observational data to learn a treatment assignment
policy that satisfies application‐specific constraints, such as budget, fairness, simplicity, or …

There has been considerable interest across several fields in methods that reduce the
problem of learning good treatment assignment policies to the problem of accurate policy …

Orthogonal statistical learning Page 1 The Annals of Statistics 2023, Vol. 51, No. 3, 879–908
https://doi.org/10.1214/23-AOS2258 © Institute of Mathematical Statistics, 2023 ORTHOGONAL …

The purpose of these lecture notes is to provide an introduction to the general theory of
empirical risk minimization with an emphasis on excess risk bounds and oracle inequalities …

Neural network in the mean-field regime is known to be capable of\textit {feature learning},
unlike the kernel (NTK) counterpart. Recent works have shown that mean-field neural …

In many settings, a decision maker wishes to learn a rule, or policy, that maps from
observable characteristics of an individual to an action. Examples include selecting offers …