An accelerated proximal alternating direction method of multipliers for robust fused Lasso
An accelerated proximal alternating direction method of multipliers for robust fused Lasso
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DOI：
10.1051/ro/2023065
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发表时间：
2023-05
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影响因子：
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通讯作者：
Yibao Fan;Youlin Shang;Zheng-Fen Jin;Jia Liu;Roxin Zhang
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文献类型：
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作者：
Yibao Fan;Youlin Shang;Zheng-Fen Jin;Jia Liu;Roxin Zhang
在大数据时代，许多数据容易受到重尾分布噪声的影响。融合Lasso算法可以有效地处理已知高斯噪声下相邻变量之间具有强相关性的高维稀疏数据。但是，它对具有重尾分布的非高斯噪声的鲁棒性较差。鲁棒的融合Lasso方法可以克服融合Lasso方法在噪声为重尾分布时的不足。但求解该模型的关键挑战是非光滑性及其不可分离性。因此，在本文中，我们首先变形的鲁棒融合Lasso到一个容易求解的形式，这改变了三块的目标函数到两块的形式。在此基础上，我们提出了一种附加更新步骤的加速邻近交替方向乘子法（APADMM），它是基于一种新的PADMM，它改变了拉格朗日乘子项的更新。此外，我们给出了所提出的APADMM的O（1/K）的非遍历收敛速度分析。最后，数值结果表明，所提出的新的PADMM和APADMM具有更好的性能比其他现有的ADMM求解器。
In the era of big data, much of the data is susceptible to noise with heavy-tailed distribution. Fused Lasso can effectively handle high dimensional sparse data with strong correlation between two adjacent variables under known Gaussian noise. However, it has poor robustness to nonGaussian noise with heavy-tailed distribution. Robust fused Lasso with l1 norm loss function can overcome the drawback of fused Lasso when noise is heavy-tailed distribution. But the key challenge for solving this model is nonsmoothness and its nonseparability. Therefore, in this paper, we first deform the robust fused Lasso into an easily solvable form, which changes the three-block objective function to a two-block form. Then, we propose an accelerated proximal alternating direction method of multipliers (APADMM) with an additional update step, which is base on a new PADMM that changes the Lagrangian multiplier term update. Furthermore, we give the O(1/K) nonergodic convergence rate analysis of the proposed APADMM. Finally, numerical results show that the proposed new PADMM and APADMM have better performance than other existing ADMM solvers.