  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

Machine Learning;Machine Learning