Rate Optimal Denoising of Simultaneously Sparse and Low Rank Matrices
arXiv:1405.0338
Abstract
We study minimax rates for denoising simultaneously sparse and low rank matrices in high dimensions. We show that an iterative thresholding algorithm achieves (near) optimal rates adaptively under mild conditions for a large class of loss functions. Numerical experiments on synthetic datasets also demonstrate the competitive performance of the proposed method.
References in corpus (9)
- Nearly unbiased variable selection under minimax concave penalty
- Sparse principal component analysis and iterative thresholding
- Sparse PCA: Optimal rates and adaptive estimation
- Truncated Power Method for Sparse Eigenvalue Problems
- Sparsity based sub-wavelength imaging with partially incoherent light via quadratic compressed sensing
- Finding large average submatrices in high dimensional data
- Minimax risk of matrix denoising by singular value thresholding
- Detection of a sparse submatrix of a high-dimensional noisy matrix
- Optimal Estimation and Completion of Matrices with Biclustering Structures
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