Robust Hierarchical-Optimization RLS Against Sparse Outliers
Robust Hierarchical-Optimization RLS Against Sparse Outliers
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DOI：
10.1109/lsp.2019.2963188
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发表时间：
2019-10
影响因子：
3.9
通讯作者：
K. Slavakis;Sinjini Banerjee
中科院分区：
文献类型：
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作者：
K. Slavakis;Sinjini Banerjee
这封信加强了最近推出的分层优化递归最小二乘（HO-RLS）对离群值污染很少线性回归模型。离群值被建模为滋扰变量，并通过稀疏诱导（非）凸正则化最小二乘任务与线性滤波器/系统变量一起估计。建议的离群鲁棒HO-RLS建立在具有恒定步长的最速下降方向上（学习率），不需要矩阵求逆（引理），适应已知相关矩阵的有色标称噪声，表现出小的计算足迹，并且在概率意义上为系统估计收敛到分层优化问题的解提供理论保证：在经典系综LS损失的最小化器上最小化凸损失，该凸损失模拟关于未知系统的先验知识。在静态和非静态的情况下，综合生成的数据进行了广泛的数值测试，展示了显着的改进，所提出的计划在国家的最先进的技术。
This letter fortifies the recently introduced hierarchical-optimization recursive least squares (HO-RLS) against outliers which contaminate infrequently linear-regression models. Outliers are modeled as nuisance variables and are estimated together with the linear filter/system variables via a sparsity-inducing (non-)convexly regularized least-squares task. The proposed outlier-robust HO-RLS builds on steepest-descent directions with a constant step size (learning rate), needs no matrix inversion (lemma), accommodates colored nominal noise of known correlation matrix, exhibits small computational footprint, and offers theoretical guarantees, in a probabilistic sense, for the convergence of the system estimates to the solutions of a hierarchical-optimization problem: Minimize a convex loss, which models a-priori knowledge about the unknown system, over the minimizers of the classical ensemble LS loss. Extensive numerical tests on synthetically generated data in both stationary and non-stationary scenarios showcase notable improvements of the proposed scheme over state-of-the-art techniques.