WebJun 25, 2013 · Our analysis brings into sharp focus the shrinkage-and-thresholding form of the optimal weights, the non-convex nature of the associated shrinkage function (on the singular values) and explains why matrix regularization via singular value thresholding with convex penalty functions (such as the nuclear norm) will always be suboptimal. WebMay 24, 2016 · In this setting, we derive generalized Stein's unbiased risk estimation (SURE) formulas that hold for any spectral estimators which shrink or threshold the singular values of the data matrix. This leads to new data-driven spectral estimators, whose optimality is discussed using tools from random matrix theory and through numerical experiments.

Code Supplement for "Optimal Shrinkage of Singular Values"

WebMar 8, 2015 · It thresholds and shrinks the singular values in a single step using two parameters that parametrize a continuum of thresholding and shrinking functions. We propose in Sect. 2.2 simple though efficient strategies to select the two tuning parameters from the data, without relying on the unstable and costly cross-validation. north middle school great falls mt website

Matrix Denoising with Partial Noise Statistics: Optimal Singular …

WebFor scalar and vector denoising, univariate shrinkage rules have proved to be simple and practical denoising methods, with near-optimal performance guarantees under various … WebThis is achieved by employing optimal shrinkage singular value decomposition (OS-SVD) [ 10] to shrink the singular values while minimizing the nuclear norm . We choose OS-SVD for its theoretically provable optimality [ 10] and the nuclear norm as the loss function for preservation of structural information [ 14 ]. WebMay 29, 2014 · Optimal Shrinkage of Singular Values. 29 May 2014 · Matan Gavish , David L. Donoho ·. Edit social preview. We consider recovery of low-rank matrices from noisy data … how to scan iambic pentameter