The Ridgeless minimum $\ell_2 $-norm interpolator in overparametrized linear regression
has attracted considerable attention in recent years. While it seems to defy the conventional …

Generalized cross-validation (GCV) is a widely used method for estimating the squared out-
of-sample prediction risk that employs scalar degrees of freedom adjustment (in a …

We employ random matrix theory to establish consistency of generalized cross validation
(GCV) for estimating prediction risks of sketched ridge regression ensembles, enabling …

We characterize the squared prediction risk of ensemble estimators obtained through
subagging (subsample bootstrap aggregating) regularized M-estimators and construct a …

We study the behavior of optimal ridge regularization and optimal ridge risk for out-of-
distribution prediction, where the test distribution deviates arbitrarily from the train …

Dataset distillation (DD) is an increasingly important technique that focuses on constructing
a synthetic dataset capable of capturing the core information in training data to achieve …

We study the implicit regularization effects induced by (observation) weighting of pretrained
features. For weight and feature matrices of bounded operator norms that are infinitesimally …

Common practice in modern machine learning involves fitting a large number of parameters
relative to the number of observations. These overparameterized models can exhibit …

This thesis delves into the spectral properties of covariance matrices and investigates the
statistical behavior of Ridge estimators in high-dimensional settings. The first part focuses on …

In this dissertation, we present several forays into the complexity that characterizes modern
machine learning, with a focus on the interplay between learning processes, incentives, and …