Confidence Intervals for Algorithmic Leveraging in Linear Regression

TL;DR

This paper develops efficient algorithms to construct finite sample confidence intervals for regression coefficients estimated via algorithmic leveraging, providing asymptotic coverage guarantees and empirical validation.

Contribution

It introduces novel algorithms for confidence interval construction in large-scale linear regression using algorithmic leveraging, with proven coverage guarantees.

Findings

Confidence intervals achieve desired coverage probabilities in simulations

Bootstrap intervals may not maintain coverage

Algorithms are computationally efficient for big data

Abstract

The age of big data has produced data sets that are computationally expensive to analyze and store. Algorithmic leveraging proposes that we sample observations from the original data set to generate a representative data set and then perform analysis on the representative data set. In this paper, we present efficient algorithms for constructing finite sample confidence intervals for each algorithmic leveraging estimated regression coefficient, with asymptotic coverage guarantees. In simulations, we confirm empirically that the confidence intervals have the desired coverage probabilities, while bootstrap confidence intervals may not.