Path Thresholding: Asymptotically Tuning-Free High-Dimensional Sparse Regression
This addresses the challenge of parameter tuning for researchers and practitioners in high-dimensional statistics, offering a computationally efficient solution, though it is incremental as it builds on existing sparse regression methods.
The paper tackles the problem of tuning parameter selection in high-dimensional sparse regression by proposing Path Thresholding (PaTh), a method that converts any tuning-dependent algorithm into an asymptotically tuning-free one, with proven accuracy under large-scale conditions and reduced computational burden in finite settings.
In this paper, we address the challenging problem of selecting tuning parameters for high-dimensional sparse regression. We propose a simple and computationally efficient method, called path thresholding (PaTh), that transforms any tuning parameter-dependent sparse regression algorithm into an asymptotically tuning-free sparse regression algorithm. More specifically, we prove that, as the problem size becomes large (in the number of variables and in the number of observations), PaTh performs accurate sparse regression, under appropriate conditions, without specifying a tuning parameter. In finite-dimensional settings, we demonstrate that PaTh can alleviate the computational burden of model selection algorithms by significantly reducing the search space of tuning parameters.