Design of $c$-Optimal Experiments for High dimensional Linear Models

TL;DR

This paper develops a method for designing optimal experiments in high-dimensional linear models to minimize estimator variance, leveraging unlabeled data and semidefinite programming.

Contribution

It introduces a novel approach for selecting sampling distributions that improve estimator efficiency using semidefinite programming in high-dimensional settings.

Findings

Optimal designs significantly reduce estimator variance.

Simulation experiments confirm efficiency improvements.

Method leverages unlabeled data effectively.

Abstract

We study random designs that minimize the asymptotic variance of a de-biased lasso estimator when a large pool of unlabeled data is available but measuring the corresponding responses is costly. The optimal sampling distribution arises as the solution of a semidefinite program. The improvements in efficiency that result from these optimal designs are demonstrated via simulation experiments.