Title: Variable selection in convex nonparametric least squares via structured Lasso: An application to the Swedish electricity distribution networks Show Chinese title

Title: 通过结构化Lasso的凸非参数最小二乘变量选择：对瑞典电力配电网络的应用

Abstract: We study the problem of variable selection in convex nonparametric least squares (CNLS). Whereas the least absolute shrinkage and selection operator (Lasso) is a popular technique for least squares, its variable selection performance is unknown in CNLS problems. In this work, we investigate the performance of the Lasso estimator and find out it is usually unable to select variables efficiently. Exploiting the unique structure of the subgradients in CNLS, we develop a structured Lasso method by combining $\ell_1$-norm and $\ell_{\infty}$-norm. The relaxed version of the structured Lasso is proposed for achieving model sparsity and predictive performance simultaneously, where we can control the two effects--variable selection and model shrinkage--using separate tuning parameters. A Monte Carlo study is implemented to verify the finite sample performance of the proposed approaches. We also use real data from Swedish electricity distribution networks to illustrate the effects of the proposed variable selection techniques. The results from the simulation and application confirm that the proposed structured Lasso performs favorably, generally leading to sparser and more accurate predictive models, relative to the conventional Lasso methods in the literature. Show Chinese abstract

Abstract: 我们研究凸非参数最小二乘（CNLS）中的变量选择问题。 尽管最小绝对收缩和选择算子（Lasso）是一种流行的最小二乘技术，但其在CNLS问题中的变量选择性能尚不清楚。 在本工作中，我们研究了Lasso估计量的性能，并发现它通常无法有效地选择变量。 利用CNLS中次梯度的独特结构，我们通过结合$\ell_1$-范数和$\ell_{\infty}$-范数开发了一种结构化Lasso方法。 提出了结构化Lasso的放松版本，以同时实现模型稀疏性和预测性能，其中我们可以使用单独的调参来控制两个效应——变量选择和模型收缩。 实施了蒙特卡洛研究以验证所提出方法的有限样本性能。 我们还使用来自瑞典电力配电网络的真实数据来说明所提出的变量选择技术的效果。 模拟和应用的结果表明，所提出的结构化Lasso表现良好，通常相对于文献中的传统Lasso方法，能够生成更稀疏和更准确的预测模型。