Accelerating ILL-Conditioned Robust Low-Rank Tensor Regression
Accelerating ILL-Conditioned Robust Low-Rank Tensor Regression
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DOI：
10.1109/icassp43922.2022.9746705
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发表时间：
2022-05
期刊：
影响因子：
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通讯作者：
Tian Tong;Cong Ma;Yuejie Chi
中科院分区：
文献类型：
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作者：
Tian Tong;Cong Ma;Yuejie Chi
信号处理，机器学习和数据科学中不同应用中出现的一个重要问题是可靠地估计可能损坏的少量测量值。有效的算法通过求解张量因子的非平滑和非凸复合优化问题，从而最小化绝对偏差损失提出的算法 - 在亚级别方法上建立，旨在等效的W.R.T。提出的算法。
An important problem that arises across different applications in signal processing, machine learning, and data science is to reliably estimate a tensor from a small number of measurements that are possibly corrupted. Leveraging the low-rank structure under the Tucker decomposition, we propose a provably efficient algorithm that directly estimates the tensor factors by solving a nonsmooth and nonconvex composite optimization problem that minimizes the least absolute deviation loss. The proposed algorithm—built on subgradient methods—harnesses preconditioners that are designed to be equivariant w.r.t. the low-rank parameterization, and is shown to achieve local linear convergence at a constant rate under the Gaussian design. Numerical experiments are provided to corroborate the superior performance of the proposed algorithm.