Keeping greed good: sparse regression under design uncertainty with application to biomass characterization
This work addresses measurement error issues in regression for applications like biomass characterization, but it is incremental as it builds on existing sparse algorithms.
The paper tackles the problem of sparse regression when design variables have measurement errors by leveraging replicated measurements to estimate and scale variances, demonstrating improved performance on a biomass characterization dataset using LARS and Dantzig selector algorithms.
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).