Robust estimation in regression and classification methods for large dimensional data
Robust estimation in regression and classification methods for large dimensional data
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DOI：
10.1007/s10994-023-06349-2
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发表时间：
2023-07
期刊：
影响因子：
7.5
通讯作者：
Chunming Zhang;Lixing Zhu;Yanbo Shen
中科院分区：
文献类型：
--
作者：
Chunming Zhang;Lixing Zhu;Yanbo Shen
统计数据分析和机器学习在很大程度上依赖于回归、分类和预测的误差度量。Bregman divergence（）是一个广泛使用的误差度量家族，但它对大型和高维数据集中的离群观测或高杠杆点不鲁棒。在本文中，我们提出了一个新的家庭的强大的Bregman分歧称为“鲁棒”，是不敏感的数据离群值。我们探讨了它们对稀疏高维回归模型的适用性与不完全指定的响应变量分布，并提出了一个新的估计称为“惩罚鲁棒估计”，实现了相同的甲骨文属性普通非鲁棒惩罚最小二乘和惩罚似然估计。我们进行了广泛的数值实验，以评估所提出的惩罚鲁棒估计的性能，并将其与经典方法进行比较，并表明我们所提出的方法改进了现有的方法。最后，我们分析了一个真实的数据集，以说明我们提出的方法的实用性。我们的研究结果表明，所提出的方法可以是一个有用的工具，强大的统计数据分析和机器学习中存在的离群值和高维数据。
Statistical data analysis and machine learning heavily rely on error measures for regression, classification, and forecasting. Bregman divergence () is a widely used family of error measures, but it is not robust to outlying observations or high leverage points in large- and high-dimensional datasets. In this paper, we propose a new family of robust Bregman divergences called “robust-” that are less sensitive to data outliers. We explore their suitability for sparse large-dimensional regression models with incompletely specified response variable distributions and propose a new estimate called the “penalized robust-estimate” that achieves the same oracle property as ordinary non-robust penalized least-squares and penalized-likelihood estimates. We conduct extensive numerical experiments to evaluate the performance of the proposed penalized robust-estimate and compare it with classical approaches, and show that our proposed method improves on existing approaches. Finally, we analyze a real dataset to illustrate the practicality of our proposed method. Our findings suggest that the proposed method can be a useful tool for robust statistical data analysis and machine learning in the presence of outliers and large-dimensional data.