Weighted Matrix Completion From Non-Random, Non-Uniform Sampling Patterns
Weighted Matrix Completion From Non-Random, Non-Uniform Sampling Patterns
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DOI：
10.1109/tit.2020.3039308
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发表时间：
2019-10
影响因子：
2.5
通讯作者：
S. Foucart;D. Needell;Reese Pathak;Y. Plan;Mary Wootters
中科院分区：
文献类型：
--
作者：
S. Foucart;D. Needell;Reese Pathak;Y. Plan;Mary Wootters
研究了观测模式为确定性且可能不均匀时的矩阵补全问题。我们提出了一种简单有效的去偏投影方案，用于从噪声观测中恢复，并在合适的加权度量下分析误差。我们介绍了权矩阵的一个简单函数和控制恢复矩阵精度的采样模式。我们得到了理论保证，恢复误差的上界和接近匹配的下界显示了几种制度下的最优性。我们的数值实验证明了我们的方法的计算效率和准确性，并表明在使用非均匀采样模式时，去偏是必不可少的。
We study the matrix completion problem when the observation pattern is deterministic and possibly non-uniform. We propose a simple and efficient debiased projection scheme for recovery from noisy observations and analyze the error under a suitable weighted metric. We introduce a simple function of the weight matrix and the sampling pattern that governs the accuracy of the recovered matrix. We derive theoretical guarantees that upper bound the recovery error and nearly matching lower bounds that showcase optimality in several regimes. Our numerical experiments demonstrate the computational efficiency and accuracy of our approach, and show that debiasing is essential when using non-uniform sampling patterns.