受损线性模型中的快速稳健最小二乘估计
Fast and Robust Least Squares Estimation in Corrupted Linear Models
摘要：
最近提出了二次抽样方法，以加快最小二乘估计在大规模设置。然而，这些算法通常对观察到的协变量中的离群值或损坏不鲁棒。影响的概念，回归诊断可以用来检测这种损坏的观察，如本文所示。这种属性的影响-我们也开发了一个随机近似-激励我们提出的子采样算法的大规模损坏的线性回归，限制了数据点的影响，因为高影响力的点贡献最大的残差。在损坏的观测的一般模型下，我们在各种模拟和真实数据集上从理论和经验上证明，我们的算法比当前最先进的普通最小二乘近似方案有所改进。
英文摘要：
Subsampling methods have been recently proposed to speed up least squares estimation in large scale settings. However, these algorithms are typically not robust to outliers or corruptions in the observed covariates. The concept of influence that was developed for regression diagnostics can be used to detect such corrupted observations as shown in this paper. This property of influence -- for which we also develop a randomized approximation -- motivates our proposed subsampling algorithm for large scale corrupted linear regression which limits the influence of data points since highly influential points contribute most to the residual error. Under a general model of corrupted observations, we show theoretically and empirically on a variety of simulated and real datasets that our algorithm improves over the current state-of-the-art approximation schemes for ordinary least squares.
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