Sparse Stable Outlier-Robust Regression with Minimax Concave Function
Sparse Stable Outlier-Robust Regression with Minimax Concave Function
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DOI：
10.1109/mlsp55214.2022.9943378
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发表时间：
2022-08
期刊：
影响因子：
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通讯作者：
Kyohei Suzuki;M. Yukawa
中科院分区：
文献类型：
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作者：
Kyohei Suzuki;M. Yukawa
我们提出了一种新的公式，用于从被异常值和严重噪声污染的测量中稳定的稀疏恢复。提出的公式分别用二次函数和极大极小凹函数来评价噪声和离群值，以反映它们的统计特性（高斯性和稀疏性）。这与传统的鲁棒方法有很大的不同，传统的鲁棒方法通常用单个损失函数来评估噪声和异常值，从而导致估计的稳定性。虽然提出的公式涉及非凸惩罚以减少稀疏估计的估计偏差，但通过添加Tikhonov正则化项，在一定条件下保证了整个代价的总体凸性。通过前向后原对偶分裂算法的重新表述来解决问题，并推导出收敛条件。高噪声环境下的仿真结果表明，该方法具有显著的离群鲁棒性。
We propose a novel formulation for stable sparse recovery from measurements contaminated by outliers and severe noise. The proposed formulation evaluates noise and outliers with a quadratic function and the minimax concave function, respectively, to reflect their statistical properties (Gaussianity and sparsity). This makes a significant difference from the conventional robust methods, which typically evaluate noise and outliers with a single loss function, leading to stability of the estimate. While the proposed formulation involves a nonconvex penalty to reduce estimation biases of sparse estimates, overall convexity of the whole cost is guaranteed under a certain condition by adding the Tikhonov regularization term. The problem is solved via a reformulation by the forward-backward primal-dual splitting algorithm, for which convergence conditions are derived. The remarkable outlier-robustness of the proposed method is demonstrated by simulations under highly noisy environments.