Generalized SURE for optimal shrinkage of singular values in low-rank matrix denoising
zbMath1440.94012arXiv1605.07412MaRDI QIDQ4637067
Charles-Alban Deledalle, Jérémie Bigot, Delphine Féral
Publication date: 17 April 2018
Full work available at URL: https://arxiv.org/abs/1605.07412
singular value decompositionexponential familyrandom matrix theorydegrees of freedomStein's unbiased risk estimatematrix denoisingspectral estimatorlow-rank modeloptimal shrinkage ruleGaussian spiked population model
Estimation in multivariate analysis (62H12) Signal theory (characterization, reconstruction, filtering, etc.) (94A12) Eigenvalues, singular values, and eigenvectors (15A18)
Related Items (5)
Uses Software
Cites Work
- Unnamed Item
- Unnamed Item
- Nonlinear shrinkage estimation of large-dimensional covariance matrices
- Adaptive shrinkage of singular values
- Reconstruction of a low-rank matrix in the presence of Gaussian noise
- The singular values and vectors of low rank perturbations of large rectangular random matrices
- Minimax risk of matrix denoising by singular value thresholding
- Selecting the number of principal components: estimation of the true rank of a noisy matrix
- Spectral analysis of large dimensional random matrices
- A fast ``Monte-Carlo cross-validation procedure for large least squares problems with noisy data
- On Kullback-Leibler loss and density estimation
- Estimation of the mean of a multivariate normal distribution
- Multivariate empirical Bayes and estimation of covariance matrices
- A natural identity for exponential families with applications in multiparameter estimation
- The Kullback-Leibler risk of the Stein estimator and the conditional MLE
- Principal component analysis.
- On the empirical distribution of eigenvalues of large dimensional information-plus-noise-type matrices
- Estimation of Kullback-Leibler losses for noisy recovery problems within the exponential family
- Eigenvalues of large sample covariance matrices of spiked population models
- On Poisson signal estimation under Kullback-Leibler discrepancy and squared risk
- Exact matrix completion via convex optimization
- Twice Differentiable Spectral Functions
- Generalized Low Rank Models
- The Optimal Hard Threshold for Singular Values is <inline-formula> <tex-math notation="TeX">\(4/\sqrt {3}\) </tex-math></inline-formula>
- OptShrink: An Algorithm for Improved Low-Rank Signal Matrix Denoising by Optimal, Data-Driven Singular Value Shrinkage
- An Introduction to Random Matrices
- Séminaire de Probabilités XXXVI
- Generalized SURE for Exponential Families: Applications to Regularization
- Unbiased Risk Estimates for Singular Value Thresholding and Spectral Estimators
- Poisson Matrix Recovery and Completion
- Optimal Shrinkage of Singular Values
- Analysis of call centre arrival data using singular value decomposition
- Empirical Bayes on vector observations: An extension of Stein's method
- The Estimation of Prediction Error
- A new look at the statistical model identification
This page was built for publication: Generalized SURE for optimal shrinkage of singular values in low-rank matrix denoising