تقرير
Matrix Denoising with Partial Noise Statistics: Optimal Singular Value Shrinkage of Spiked F-Matrices
| العنوان: | Matrix Denoising with Partial Noise Statistics: Optimal Singular Value Shrinkage of Spiked F-Matrices |
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| المؤلفون: | Gavish, Matan, Leeb, William, Romanov, Elad |
| المصدر: | Information and Inference: A Journal of the IMA, Volume 12, Issue 3, September 2023, iaad028 |
| سنة النشر: | 2022 |
| المجموعة: | Computer Science Mathematics Statistics |
| مصطلحات موضوعية: | Mathematics - Statistics Theory, Computer Science - Information Theory, Electrical Engineering and Systems Science - Signal Processing |
| الوصف: | 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. |
| نوع الوثيقة: | Working Paper |
| DOI: | 10.1093/imaiai/iaad028 |
| URL الوصول: | http://arxiv.org/abs/2211.00986 |
| رقم الأكسشن: | edsarx.2211.00986 |
| قاعدة البيانات: | arXiv |
| DOI: | 10.1093/imaiai/iaad028 |
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