论文标题
Huber标准的块最小化算法：稀疏学习和应用
Block-wise Minimization-Majorization algorithm for Huber's criterion: sparse learning and applications
论文作者
论文摘要
Huber的标准可用于线性模型中回归和比例参数的鲁棒关节估计。 Huber（Huber，1981）引入标准的动机是源于关节最大似然目标函数的非跨性别性以及相关的ML尺度ML的非稳定性（无界影响函数）。在本文中，我们说明了如何将Huber提出的原始算法设置在块最小化的主要化框架内。此外，我们提出了针对位置和尺度的新型数据自适应步进大小，这进一步改善了收敛性。然后，我们说明如何使用迭代的硬阈值方法将Huber的标准用于稀疏学习不确定的线性模型。我们说明了算法在图像deo的应用和仿真研究中的有用性。
Huber's criterion can be used for robust joint estimation of regression and scale parameters in the linear model. Huber's (Huber, 1981) motivation for introducing the criterion stemmed from non-convexity of the joint maximum likelihood objective function as well as non-robustness (unbounded influence function) of the associated ML-estimate of scale. In this paper, we illustrate how the original algorithm proposed by Huber can be set within the block-wise minimization majorization framework. In addition, we propose novel data-adaptive step sizes for both the location and scale, which are further improving the convergence. We then illustrate how Huber's criterion can be used for sparse learning of underdetermined linear model using the iterative hard thresholding approach. We illustrate the usefulness of the algorithms in an image denoising application and simulation studies.
