Accuracy and stability of solar variable selection comparison under complicated dependence structures

TL;DR

This paper evaluates the Solar variable selection method, a novel ultrahigh-dimensional approach, demonstrating its superior stability, accuracy, and robustness over traditional lasso methods under complex dependence structures in empirical data.

Contribution

The paper introduces and empirically validates Solar as a robust, efficient alternative to lasso for variable selection in high-dimensional data with complicated dependence structures.

Findings

Solar reduces the number of selected variables by 37-64%.

Solar outperforms lasso and elastic net in stability and accuracy.

Solar is more robust to dependence structures and grouping effects.

Abstract

In this paper we focus on the empirical variable-selection peformance of subsample-ordered least angle regression (Solar) -- a novel ultrahigh dimensional redesign of lasso -- on the empirical data with complicated dependence structures and, hence, severe multicollinearity and grouping effect issues. Previous researches show that Solar largely alleviates several known high-dimensional issues with least-angle regression and $\mathcal{L}_1$ shrinkage. Also, With the same computation load, solar yields substantiali mprovements over two lasso solvers (least-angle regression for lasso and coordinate-descent) in terms of the sparsity (37-64\% reduction in the average number of selected variables), stability and accuracy of variable selection. Simulations also demonstrate that solar enhances the robustness of variable selection to different settings of the irrepresentable condition and to variations in the dependence structures assumed in regression analysis. To confirm that the improvements are also available for empirical researches, we choose the prostate cancer data and the Sydney house price data and apply two lasso solvers, elastic net and Solar on them for comparison. The results shows that (i) lasso is affected by the grouping effect and randomly drop variables with high correlations, resulting unreliable and uninterpretable results; (ii) elastic net is more robust to grouping effect; however, it completely lose variable-selection sparsity when the dependence structure of the data is complicated; (iii) solar demonstrates its superior robustness to complicated dependence structures and grouping effect, returning variable-selection results with better stability and sparsity. The code can be found at https://github.com/isaac2math/solar_application