Stable Robust Regression under Sparse Outlier and Gaussian Noise
Stable Robust Regression under Sparse Outlier and Gaussian Noise
复制标题
稀疏异常值和高斯噪声下的稳定鲁棒回归
DOI：
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发表时间：
2022
期刊：
影响因子：
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通讯作者：
I. Yamada
中科院分区：
文献类型：
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作者：
M. Yukawa;Kyohei Suzuki;I. Yamada
我们提出了一种高效的回归方法，该方法对异常值具有很强的鲁棒性，即使在严重噪声的情况下也是稳定的。这里的稳健性来自于最小极大凹损失的采用，而稳定性来自于通过引入模拟高斯噪声的辅助向量来分别处理孤立点和噪声。在一定的假设条件下，我们给出了总费用的光滑部分凸性的充要条件，其中一般模型具有潜在的应用前景。我们证明了在凸性条件下，所提出的公式可以用基于正向-反向的原始-对偶方法进行重写来求解。数值算例表明，该估计器在高噪声环境下具有显著的鲁棒性。
We propose an efficient regression method which is highly robust against outliers and stable even in the severely noisy situations. The robustness here comes from the adoption of the minimax concave loss, while the stability comes from separate treatments of the outlier and noise by an introduction of an auxiliary vector modeling the Gaussian noise. We present a necessary and sufficient condition for convexity of the smooth part of the entire cost under a certain assumption, where a general model is used with its potential use for other applications envisioned. We show that the proposed formulation can be solved via reformulation by the forward-backward-based primal-dual method under the convexity condition. The numerical examples show the remarkable robustness of the proposed estimator under highly noisy situations.