论文标题
IRL的全球线性和局部超级线性收敛，用于非平滑鲁棒回归
Global Linear and Local Superlinear Convergence of IRLS for Non-Smooth Robust Regression
论文作者
论文摘要
我们通过使用迭代重新加权的最小二乘（IRLS）的新颖变体来解决基本的非平滑问题。在convex案例中，$ p = 1 $，我们在全球范围内确定互惠率的范围，我们可以在（0,1] $ in（0,1）$中推进（0,1）$的理论和实践。矩阵称为\ textIt {稳定范围属性}，在非凸件中，$ p \ in（0,1）$，我们证明，在类似的条件下，irls以$ 2-p $ question coption coption coption cosection coption coption coption coption coption and coption and coption and coption and coption and coption and Inters and thress and offection。强大的脸部恢复表明，（1）IRL可以处理更多的离群值，（2）它比在同一准确度上的竞争方法更快，（3）它以令人满意的视觉质量恢复了稀疏的脸部图像
We advance both the theory and practice of robust $\ell_p$-quasinorm regression for $p \in (0,1]$ by using novel variants of iteratively reweighted least-squares (IRLS) to solve the underlying non-smooth problem. In the convex case, $p=1$, we prove that this IRLS variant converges globally at a linear rate under a mild, deterministic condition on the feature matrix called the \textit{stable range space property}. In the non-convex case, $p\in(0,1)$, we prove that under a similar condition, IRLS converges locally to the global minimizer at a superlinear rate of order $2-p$; the rate becomes quadratic as $p\to 0$. We showcase the proposed methods in three applications: real phase retrieval, regression without correspondences, and robust face restoration. The results show that (1) IRLS can handle a larger number of outliers than other methods, (2) it is faster than competing methods at the same level of accuracy, (3) it restores a sparsely corrupted face image with satisfactory visual quality. https://github.com/liangzu/IRLS-NeurIPS2022
