Approximately low-rank recovery from noisy and local measurements by convex program
Approximately low-rank recovery from noisy and local measurements by convex program
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通过凸程序从噪声和局部测量中近似低秩恢复
DOI：
10.1093/imaiai/iaad013
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发表时间：
2023
期刊：
影响因子：
--
通讯作者：
Romberg, Justin
中科院分区：
文献类型：
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作者：
Lee, Kiryung;Sharma, Rakshith Srinivasa;Junge, Marius;Romberg, Justin
低秩矩阵模型已经普遍适用于许多应用，从经典的系统识别到信号处理和统计中的更现代的矩阵补全。由于核范数可以导出反问题的低秩解，因此它被用作低秩的凸替代。虽然低秩的核范数与通过奇异值分解的稀疏性定理有很好的相似性，但其他矩阵范数也会导致低秩。特别是当我们将矩阵解释为Banach空间之间的线性算子时，各种张量积范数推广了核范数的作用。我们提供了一个张量范数约束估计恢复近似低秩矩阵从本地测量损坏的噪声。张量范数正则化器的设计，以适应当地的结构。通过将Maurey的经验方法应用于Banach空间的张量积，我们推导出矩阵完备和分散草图上估计量的统计分析。估计提供了一个近似最优的误差界在极大极小意义上，并承认这些应用程序的多项式时间算法。
Low-rank matrix models have been universally useful for numerous applications, from classical system identification to more modern matrix completion in signal processing and statistics. The nuclear norm has been employed as a convex surrogate of the low-rankness since it induces a low-rank solution to inverse problems. While the nuclear norm for low rankness has an excellent analogy with thenorm for sparsity through the singular value decomposition, other matrix norms also induce low-rankness. Particularly as one interprets a matrix as a linear operator between Banach spaces, various tensor product norms generalize the role of the nuclear norm. We provide a tensor-norm-constrained estimator for the recovery of approximately low-rank matrices from local measurements corrupted with noise. A tensor-norm regularizer is designed to adapt to the local structure. We derive statistical analysis of the estimator over matrix completion and decentralized sketching by applying Maurey’s empirical method to tensor products of Banach spaces. The estimator provides a near-optimal error bound in a minimax sense and admits a polynomial-time algorithm for these applications.
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DOI：
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发表时间：
2019-02
期刊：
--
影响因子：
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作者：
Seyedehsara Nayer;Namrata Vaswani;Yonina C. Eldar
通讯作者：
Seyedehsara Nayer;Namrata Vaswani;Yonina C. Eldar
Banach空间中Bernstein-Jackson型不等式与算子的紧度
DOI：
10.5802/aif.1020
发表时间：
1985
期刊：
Annales de l'Institut Fourier
影响因子：
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作者：
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通讯作者：
B. Carl
DOI：
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发表时间：
2020-05
期刊：
J. Mach. Learn. Res.
影响因子：
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作者：
Tian Tong;Cong Ma;Yuejie Chi
通讯作者：
Tian Tong;Cong Ma;Yuejie Chi
影响因子：
1
作者：
M. Talagrand
通讯作者：
M. Talagrand
Banach空间张量积的熵估计及其在低阶恢复中的应用
DOI：
10.1109/sampta45681.2019.9030989
发表时间：
2020
期刊：
2019 13th International conference on Sampling Theory and Applications (SampTA
影响因子：
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作者：
Lee, Kiryung;Srinivasa, Rakshith Sharma;Junge, Marius;Romberg, Justin
通讯作者：
Romberg, Justin