A Framework for Sample Efficient Interval Estimation with Control Variates

TL;DR

This paper introduces a new estimation framework that leverages control variates and order statistics to produce more efficient confidence intervals for the mean, especially when side information is available, outperforming existing methods.

Contribution

It presents a novel algorithm that exploits control variates and order statistics to improve the efficiency of interval estimation under certain conditions.

Findings

Improved asymptotic efficiency over existing algorithms.

Demonstrated superior empirical performance on real-world tasks.

Effectively utilizes regression model outputs as control variates.

Abstract

We consider the problem of estimating confidence intervals for the mean of a random variable, where the goal is to produce the smallest possible interval for a given number of samples. While minimax optimal algorithms are known for this problem in the general case, improved performance is possible under additional assumptions. In particular, we design an estimation algorithm to take advantage of side information in the form of a control variate, leveraging order statistics. Under certain conditions on the quality of the control variates, we show improved asymptotic efficiency compared to existing estimation algorithms. Empirically, we demonstrate superior performance on several real world surveying and estimation tasks where we use the output of regression models as the control variates.