Robust Regression via Heuristic Hard Thresholding
Robust Regression via Heuristic Hard Thresholding
复制标题
通过启发式硬阈值进行稳健回归
DOI：
10.24963/ijcai.2017/480
复制
发表时间：
2017
期刊：
影响因子：
--
通讯作者：
Chang
中科院分区：
文献类型：
--
作者：
Xuchao Zhang;Liang Zhao;Arnold P. Boedihardjo;Chang
最近，数据噪声和腐败的存在引起了人们对鲁棒最小二乘回归（RLSR）的越来越多的关注，它解决了当响应变量可以任意腐败时学习可靠回归系数的基本问题。到目前为止，几个重要的挑战仍然无法同时处理：1）回归系数的精确恢复保证; 2）估计腐败率参数的困难;以及3）对大规模数据集的可扩展性。本文提出了一种新的鲁棒最小二乘回归算法通过启发式硬阈值（RLHH），同时解决所有上述挑战。具体地说，该算法交替优化回归系数，并通过启发式硬阈值估计的最佳未损坏的设置，没有腐败率参数，直到它收敛。我们还证明了我们的算法的好处，类似于那些国家的最先进的方法在收敛速度和恢复保证强有力的保证。实验结果表明，该方法在恢复回归系数和恢复未损坏数据集方面均优于现有方法，具有上级的性能。
The presence of data noise and corruptions recently invokes increasing attention on Robust Least Squares Regression (RLSR), which addresses the fundamental problem that learns reliable regression coefficients when response variables can be arbitrarily corrupted. Until now, several important challenges still cannot be handled concurrently: 1) exact recovery guarantee of regression coefficients 2) difficulty in estimating the corruption ratio parameter; and 3) scalability to massive dataset. This paper proposes a novel Robust Least squares regression algorithm via Heuristic Hard thresholding (RLHH), that concurrently addresses all the above challenges. Specifically, the algorithm alternately optimizes the regression coefficients and estimates the optimal uncorrupted set via heuristic hard thresholding without corruption ratio parameter until it converges. We also prove that our algorithm benefits from strong guarantees analogous to those of state-of-the-art methods in terms of convergence rates and recovery guarantees. Extensive experiment demonstrates that the effectiveness of our new method is superior to that of existing methods in the recovery of both regression coefficients and uncorrupted sets, with very competitive efficiency.