It is known that the Thresholded Lasso (TL), SCAD or MCP correct intrinsic estimation bias of the Lasso. In this paper we propose an alternative method of improving the Lasso for predictive models with general convex loss functions which encompass normal linear models, logistic regression, quantile regression, or support vector machines. For a given penalty we order the absolute values of the Lasso nonzero coefficients and then select the final model from a small nested family by the Generalized Information Criterion. We derive exponential upper bounds on the selection error of the method. These results confirm that, at least for normal linear models, our algorithm seems to be the benchmark for the theory of model selection as it is constructive, computationally efficient and leads to consistent model selection under weak assumptions. Constructivity of the algorithm means that, in contrast to the TL, SCAD or MCP, consistent selection does not rely on the unknown parameters as the cone invertibility factor. Instead, our algorithm only needs the sample size, the number of predictors and an upper bound on the noise parameter. We show in numerical experiments on synthetic and real-world datasets that an implementation of our algorithm is more accurate than implementations of studied concave regularizations. Our procedure is included in the R package DMRnet and available in the CRAN repository.

中文翻译：

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改进 Lasso 以进行模型选择和预测

众所周知，阈值套索 (TL)、SCAD 或 MCP 可以纠正套索的内在估计偏差。在本文中，我们提出了一种改进 Lasso 的替代方法，用于具有一般凸损失函数的预测模型，包括正态线性模型、逻辑回归、分位数回归或支持向量机。对于给定的惩罚，我们对 Lasso 非零系数的绝对值进行排序，然后通过广义信息准则从一个小的嵌套族中选择最终模型。我们推导出该方法的选择误差的指数上限。这些结果证实，至少对于正常的线性模型，我们的算法似乎是模型选择理论的基准，因为它具有建设性、计算效率高，并在弱假设下导致一致的模型选择。算法的构造性意味着，与 TL、SCAD 或 MCP 相比，一致选择不依赖于未知参数作为圆锥可逆性因子。相反，我们的算法只需要样本大小、预测变量的数量和噪声参数的上限。我们在合成和真实世界数据集的数值实验中表明，我们算法的实现比所研究的凹正则化的实现更准确。我们的程序包含在 R 包中 我们在合成和真实世界数据集的数值实验中表明，我们算法的实现比所研究的凹正则化的实现更准确。我们的程序包含在 R 包中 我们在合成和真实世界数据集的数值实验中表明，我们算法的实现比所研究的凹正则化的实现更准确。我们的程序包含在 R 包中DMRnet并在 CRAN 存储库中可用。