AN ITERATIVE HARD THRESHOLDING ESTIMATOR FOR LOW RANK MATRIX RECOVERY WITH EXPLICIT LIMITING DISTRIBUTION
AN ITERATIVE HARD THRESHOLDING ESTIMATOR FOR LOW RANK MATRIX RECOVERY WITH EXPLICIT LIMITING DISTRIBUTION
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DOI：
10.5705/ss.202016.0103
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发表时间：
2018-07-01
影响因子：
1.4
通讯作者：
Kim, Arlene K. H.
中科院分区：
文献类型：
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作者：
Carpentier, Alexandra;Kim, Arlene K. H.
我们考虑随机噪声高维环境中的低秩矩阵恢复问题。我们提出了一种新的估计的低秩矩阵，基于迭代硬阈值方法，这是计算效率和简单。我们证明了我们的估计是最佳的Frobenius风险和条目明智的风险一致的正交基的任何变化，使我们能够提供的极限分布的估计。当设计是高斯分布时，我们证明了估计量的极限分布的条目偏差是小的，这对于构造低秩矩阵条目的低维子集的检验和置信集是有意义的。
We consider the problem of low rank matrix recovery in a stochastically noisy high-dimensional setting. We propose a new estimator for the low rank matrix, based on the iterative hard thresholding method, that is computationally efficient and simple. We prove that our estimator is optimal in terms of the Frobenius risk and in terms of the entry-wise risk uniformly over any change of orthonormal basis, allowing us to provide the limiting distribution of the estimator. When the design is Gaussian, we prove that the entry-wise bias of the limiting distribution of the estimator is small, which is of interest for constructing tests and confidence sets for low-dimensional subsets of entries of the low rank matrix.