Keeping greed good: sparse regression under design uncertainty with application to biomass characterization

TL;DR

This paper improves sparse regression methods in the presence of measurement errors by leveraging replicated measurements to estimate variance and scale variables, demonstrated on biomass data.

Contribution

It introduces a variance estimation and scaling approach for sparse regression under design uncertainty, validated with empirical biomass data.

Findings

Scaling improves regression accuracy in noisy measurements

Method enhances LARS and Dantzig selector performance

Empirical validation confirms effectiveness on biomass data

Abstract

In this paper, we consider the classic measurement error regression scenario in which our independent, or design, variables are observed with several sources of additive noise. We will show that our motivating example's replicated measurements on both the design and dependent variables may be leveraged to enhance a sparse regression algorithm. Specifically, we estimate the variance and use it to scale our design variables. We demonstrate the efficacy of scaling from several points of view and validate it empirically with a biomass characterization data set using two of the most widely used sparse algorithms: least angle regression (LARS) and the Dantzig selector (DS).