We consider linear regression problems with a varying number of random projections,
where we provably exhibit a double descent curve for a fixed prediction problem, with a high …

We examine generalized and leave-one-out cross-validation for ridge regression in a
proportional asymptotic framework where the dimension of the feature space grows …

With the massive release of microplastics (MPs) into the environment, research related to
MPs is advancing rapidly. Effective research methods are necessary to identify the chemical …

The progress of precision medicine research hinges on the gathering and analysis of
extensive and diverse clinical datasets. With the continued expansion of modalities, scales …

Distributed linear regression by averaging Page 1 The Annals of Statistics 2021, Vol. 49, No. 2,
918–943 https://doi.org/10.1214/20-AOS1984 © Institute of Mathematical Statistics, 2021 …

Modern machine learning methods are often overparametrized, allowing adaptation to the
data at a fine level. This can seem puzzling; in the worst case, such models do not need to …

We establish precise structural and risk equivalences between subsampling and ridge
regularization for ensemble ridge estimators. Specifically, we prove that linear and quadratic …

We study the following three fundamental problems about ridge regression:(1) what is the
structure of the estimator?(2) how to correctly use cross-validation to choose the …

Bagging is a commonly used ensemble technique in statistics and machine learning to
improve the performance of prediction procedures. In this paper, we study the prediction risk …

In many areas, practitioners need to analyze large data sets that challenge conventional
single-machine computing. To scale up data analysis, distributed and parallel computing …