论文标题
与部分噪声统计数据矩阵Denoising：峰值F-矩阵的最佳单数值收缩
Matrix Denoising with Partial Noise Statistics: Optimal Singular Value Shrinkage of Spiked F-Matrices
论文作者
论文摘要
我们研究了一个估计一个由未知协方差的加性噪声损坏的大，低级别矩阵的问题，假设一个人可以以仅噪声测量的形式访问其他侧面信息。我们研究了白色碎片 - 鲜味（WSC）工作流程，其中将“噪声协方差增白”转化应用于观测值，然后进行适当的奇异值收缩和“噪声协方差重新颜色”转换。我们表明，在均方误差损失下，WSC DeNoising工作流程存在一种独特的，渐近的最佳收缩非线性，并以封闭形式进行计算。为此，我们计算了随机尖峰F-Matrix集合的渐近特征向量旋转，这可能具有独立感兴趣。有了足够多的纯噪声测量，我们最佳调整的WSC DeNoRISING工作流程的表现优于卑鄙的正方形误差，基于最佳奇异值收缩的矩阵Deno算法，这些算法不会类似地使用噪声侧面信息；数值实验表明，我们的程序的相对性能在具有较高维度和较大异质性的挑战性统计环境中尤为强。
We study the problem of estimating a large, low-rank matrix corrupted by additive noise of unknown covariance, assuming one has access to additional side information in the form of noise-only measurements. We study the Whiten-Shrink-reColor (WSC) workflow, where a "noise covariance whitening" transformation is applied to the observations, followed by appropriate singular value shrinkage and a "noise covariance re-coloring" transformation. We show that under the mean square error loss, a unique, asymptotically optimal shrinkage nonlinearity exists for the WSC denoising workflow, and calculate it in closed form. To this end, we calculate the asymptotic eigenvector rotation of the random spiked F-matrix ensemble, a result which may be of independent interest. With sufficiently many pure-noise measurements, our optimally-tuned WSC denoising workflow outperforms, in mean square error, matrix denoising algorithms based on optimal singular value shrinkage which do not make similar use of noise-only side information; numerical experiments show that our procedure's relative performance is particularly strong in challenging statistical settings with high dimensionality and large degree of heteroscedasticity.
