Fast and Robust Least Squares Estimation in Corrupted Linear Models
Fast and Robust Least Squares Estimation in Corrupted Linear Models
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发表时间：
2014-06
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通讯作者：
B. McWilliams;Gabriel Krummenacher;Mario Lucic;J. Buhmann
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作者：
B. McWilliams;Gabriel Krummenacher;Mario Lucic;J. Buhmann
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。为回归诊断而开发的影响的概念可以用于检测本文所示的这种损坏的观测。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。在一个一般模型的损坏的观察，我们表明理论和经验上的各种模拟和真实的数据集，我们的算法改进了目前的国家最先进的近似方案的普通最小二乘。
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.