复杂相关结构下太阳变星选择比较的精度和稳定性
Accuracy and stability of solar variable selection comparison under complicated dependence structures
摘要：
在本文中，我们专注于子样本有序最小角度回归（太阳能）的经验变量选择概率-一种新的三维重新设计的套索-经验数据具有复杂的依赖结构，因此，严重的多重共线性和分组效应问题。以往的研究表明，Solar在很大程度上用最小角回归和$\mathcal{L}_1$收缩来解决几个已知的高维问题。在相同的计算量下，solar在稀疏性（平均选择变量数减少37- 64%）、稳定性和变量选择的准确性方面比两种lasso求解器（lasso的最小角度回归和坐标下降）有了很大的改进。模拟还表明，太阳能增强了变量选择的鲁棒性，以不同的设置的不可表示的条件和变化的依赖结构假设在回归分析。为了验证改进的方法也适用于实证研究，我们选取了前列腺癌数据和悉尼房价数据，并应用弹性网和Solar两种套索解算器进行比较。结果表明：lasso算法受分组效应的影响，随机丢弃相关性强的变量，结果不可靠且不可解释;弹性网对分组效应具有较强的鲁棒性，但当数据的依赖结构复杂时，它完全丧失了变量选择的稀疏性;（iii）太阳能显示出其对复杂的依赖结构和分组效应的优越鲁棒性，返回具有更好的稳定性和稀疏性的变量选择结果。代码可以在https://github.com/isaac2math/solar_application上找到
英文摘要：
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
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
