论文标题
高维级别套索问题的高效基于适应性赛的算法
A Highly Efficient Adaptive-Sieving-Based Algorithm for the High-Dimensional Rank Lasso Problem
论文作者
论文摘要
高维等级拉索（HDR LASSO）模型是处理高维数据分析的有效方法。它被认为是用于高维回归的一种无调的健壮方法，并被证明比其他方法具有多种统计优势。 HDR LASSO问题本质上是$ L_1 $调查的优化问题，其损失功能是Jaeckel的分散功能，具有Wilcoxon分数。由于上述损失函数的非不同性，套索型问题的许多经典算法无法解决该模型。在本文中，受到独家套索问题的自适应筛分策略的启发[1]，我们提出了一种基于自适应的算法来解决HDR Lasso问题。提出的算法充分利用了溶液的稀疏性。在每次迭代中，解决了与原始模型相同形式的子问题，但尺寸要小得多。我们应用近端算法来解决子问题，该子问题充分利用了两个非平滑项。广泛的数值结果表明，所提出的算法（AS-PPA）对于不同类型的噪声是可靠的，该噪声验证了[2]中所示的有吸引力的统计特性。此外，与其他方法相比，AS-PPA也很高，尤其是对于高维特征的情况。
The high-dimensional rank lasso (hdr lasso) model is an efficient approach to deal with high-dimensional data analysis. It was proposed as a tuning-free robust approach for the high-dimensional regression and was demonstrated to enjoy several statistical advantages over other approaches. The hdr lasso problem is essentially an $L_1$-regularized optimization problem whose loss function is Jaeckel's dispersion function with Wilcoxon scores. Due to the nondifferentiability of the above loss function, many classical algorithms for lasso-type problems are unable to solve this model. In this paper, inspired by the adaptive sieving strategy for the exclusive lasso problem [1], we propose an adaptive-sieving-based algorithm to solve the hdr lasso problem. The proposed algorithm makes full use of the sparsity of the solution. In each iteration, a subproblem with the same form as the original model is solved, but in a much smaller size. We apply the proximal point algorithm to solve the subproblem, which fully takes advantage of the two nonsmooth terms. Extensive numerical results demonstrate that the proposed algorithm (AS-PPA) is robust for different types of noises, which verifies the attractive statistical property as shown in [2]. Moreover, AS-PPA is also highly efficient, especially for the case of high-dimensional features, compared with other methods.
