论文标题
通过非沉淀性质和实施研究，强大的融合拉索惩罚了Huber回归
Robust Fused Lasso Penalized Huber Regression with Nonasymptotic Property and Implementation Studies
论文作者
论文摘要
对于现实中的一些特殊数据，例如遗传数据，相邻基因可能具有相似的功能。因此，非常必要确保相邻基因之间的平滑度。但是，在这种情况下，标准的拉索罚款似乎不再合适。另一方面，在高维统计中，某些数据集很容易被异常值污染或包含具有重尾分布的变量，这使得许多常规方法不足。为了解决这两个问题，在本文中，我们提出了一种自适应的Huber回归，以进行稳健的估计和推理，其中使用融合的套索罚款来鼓励系数的稀疏性以及它们差异的稀疏性，即系数的局部构造。从理论上讲，我们在$ \ ell_2 $ norm下在高维设置下建立了其非反应估计误差界限。所提出的估计方法被配制为凸，非滑动和可分离的优化问题，因此可以采用乘数的交替方向方法。最后，我们对仿真研究和实际癌症数据研究进行了执行，这表明所提出的估计方法更鲁棒和预测。
For some special data in reality, such as the genetic data, adjacent genes may have the similar function. Thus ensuring the smoothness between adjacent genes is highly necessary. But, in this case, the standard lasso penalty just doesn't seem appropriate anymore. On the other hand, in high-dimensional statistics, some datasets are easily contaminated by outliers or contain variables with heavy-tailed distributions, which makes many conventional methods inadequate. To address both issues, in this paper, we propose an adaptive Huber regression for robust estimation and inference, in which, the fused lasso penalty is used to encourage the sparsity of the coefficients as well as the sparsity of their differences, i.e., local constancy of the coefficient profile. Theoretically, we establish its nonasymptotic estimation error bounds under $\ell_2$-norm in high-dimensional setting. The proposed estimation method is formulated as a convex, nonsmooth and separable optimization problem, hence, the alternating direction method of multipliers can be employed. In the end, we perform on simulation studies and real cancer data studies, which illustrate that the proposed estimation method is more robust and predictive.
