[Normes de sous-matrices aléatoires et approximation creuse]
De nombreux problèmes en théorie de l'approximation non linéaire exigent des majorations la norme d'une matrice aléatoirement extraite d'une matrice donnée de plus grande dimension. L'objectif de cette Note est de présenter des estimations de ces normes qui se révèlent être importantes pour l'étude des algorithmes de minimisation de type
Many problems in the theory of sparse approximation require bounds on operator norms of a random submatrix drawn from a fixed matrix. The purpose of this Note is to collect estimates for several different norms that are most important in the analysis of
Accepté le :
Publié le :
Joel A. Tropp 1
@article{CRMATH_2008__346_23-24_1271_0, author = {Joel A. Tropp}, title = {Norms of random submatrices and sparse approximation}, journal = {Comptes Rendus. Math\'ematique}, pages = {1271--1274}, publisher = {Elsevier}, volume = {346}, number = {23-24}, year = {2008}, doi = {10.1016/j.crma.2008.10.008}, language = {en}, }
Joel A. Tropp. Norms of random submatrices and sparse approximation. Comptes Rendus. Mathématique, Volume 346 (2008) no. 23-24, pp. 1271-1274. doi : 10.1016/j.crma.2008.10.008. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2008.10.008/
[1] Invertibility of “large” submatrices with applications to the geometry of Banach spaces and harmonic analysis, Israel J. Math., Volume 57 (1987) no. 2, pp. 137-224
[2] Operator Khintchine inequality in non-commutative probability, Math. Ann., Volume 319 (2001), pp. 1-16
[3] Probability in Banach Spaces: Isoperimetry and Processes, Springer, 1991
[4] Sampling from large matrices: An approach through geometric functional analysis, J. Assoc. Comput. Mach., Volume 54 (2007) no. 4, pp. 1-19
[5] The random paving property for uniformly bounded matrices, Studia Math., Volume 185 (2008) no. 1, pp. 67-82
- Hamiltonicity of sparse pseudorandom graphs, Combinatorics, Probability and Computing (2025), p. 1 | DOI:10.1017/s0963548325000070
- The impact of contamination and correlated design on the Lasso: An average case analysis, Statistics Probability Letters, Volume 223 (2025), p. 110417 | DOI:10.1016/j.spl.2025.110417
- Sublinear Time Eigenvalue Approximation via Random Sampling, Algorithmica, Volume 86 (2024) no. 6, p. 1764 | DOI:10.1007/s00453-024-01208-5
- Norms of structured random matrices, Mathematische Annalen, Volume 388 (2024) no. 4, p. 3463 | DOI:10.1007/s00208-023-02599-6
- Average Performance of OMP and Thresholding Under Dictionary Mismatch, IEEE Signal Processing Letters, Volume 29 (2022), p. 1077 | DOI:10.1109/lsp.2022.3167313
- Incoherence is Sufficient for Statistical RIP of Unit Norm Tight Frames: Constructions and Properties, IEEE Transactions on Signal Processing, Volume 69 (2021), p. 2343 | DOI:10.1109/tsp.2021.3066777
- Submatrices with NonUniformly Selected Random Supports and Insights into Sparse Approximation, SIAM Journal on Matrix Analysis and Applications, Volume 42 (2021) no. 3, p. 1268 | DOI:10.1137/20m1386384
- , 2020 IEEE 61st Annual Symposium on Foundations of Computer Science (FOCS) (2020), p. 1191 | DOI:10.1109/focs46700.2020.00114
- , 2019 53rd Asilomar Conference on Signals, Systems, and Computers (2019), p. 271 | DOI:10.1109/ieeeconf44664.2019.9048928
- On a new method for controlling the entire spectrum in the problem of column subset selection, Expositiones Mathematicae, Volume 37 (2019) no. 3, p. 314 | DOI:10.1016/j.exmath.2019.02.002
- Construction of highly redundant incoherent unit norm tight frames as a union of orthonormal bases, Journal of Complexity, Volume 54 (2019), p. 101401 | DOI:10.1016/j.jco.2019.03.001
- Sparse signal recovery via non-convex optimization and overcomplete dictionaries, International Journal of Wavelets, Multiresolution and Information Processing, Volume 16 (2018) no. 06, p. 1850058 | DOI:10.1142/s0219691318500583
- Feature Selection in Weakly Coherent Matrices, Latent Variable Analysis and Signal Separation, Volume 10891 (2018), p. 127 | DOI:10.1007/978-3-319-93764-9_13
- An Elementary Approach to the Problem of Column Selection in a Rectangular Matrix, Machine Learning, Optimization, and Big Data, Volume 10710 (2018), p. 234 | DOI:10.1007/978-3-319-72926-8_20
- , 2017 IEEE International Workshop on Applied Measurements for Power Systems (AMPS) (2017), p. 1 | DOI:10.1109/amps.2017.8078349
- Joint Sensing Matrix and Sparsifying Dictionary Optimization for Tensor Compressive Sensing, IEEE Transactions on Signal Processing, Volume 65 (2017) no. 14, p. 3632 | DOI:10.1109/tsp.2017.2699639
- Conditioning of Random Block Subdictionaries With Applications to Block-Sparse Recovery and Regression, IEEE Transactions on Information Theory, Volume 61 (2015) no. 7, p. 4060 | DOI:10.1109/tit.2015.2429632
- Restricted Isometry Property of Random Subdictionaries, IEEE Transactions on Information Theory, Volume 61 (2015) no. 8, p. 4440 | DOI:10.1109/tit.2015.2448658
- Randomized block Kaczmarz method with projection for solving least squares, Linear Algebra and its Applications, Volume 484 (2015), p. 322 | DOI:10.1016/j.laa.2015.06.027
- Consistency ofℓ1recovery from noisy deterministic measurements, Applied and Computational Harmonic Analysis, Volume 36 (2014) no. 3, p. 508 | DOI:10.1016/j.acha.2013.08.001
- Unitary Precoding and Basis Dependency of MMSE Performance for Gaussian Erasure Channels, IEEE Transactions on Information Theory, Volume 60 (2014) no. 11, p. 7186 | DOI:10.1109/tit.2014.2354034
- Sparse Recovery With Unknown Variance: A LASSO-Type Approach, IEEE Transactions on Information Theory, Volume 60 (2014) no. 7, p. 3970 | DOI:10.1109/tit.2014.2301162
- Paved with good intentions: Analysis of a randomized block Kaczmarz method, Linear Algebra and its Applications, Volume 441 (2014), p. 199 | DOI:10.1016/j.laa.2012.12.022
- Advanced Tools from Probability Theory, A Mathematical Introduction to Compressive Sensing (2013), p. 201 | DOI:10.1007/978-0-8176-4948-7_8
- Recovery of Random Signals using Deterministic Matrices, A Mathematical Introduction to Compressive Sensing (2013), p. 459 | DOI:10.1007/978-0-8176-4948-7_14
- Performance of the Delsarte-Goethals Frame on Clustered Sparse Vectors, IEEE Transactions on Signal Processing, Volume 61 (2013) no. 8, p. 1998 | DOI:10.1109/tsp.2013.2242064
- Sharp support recovery from noisy random measurements byℓ1-minimization, Applied and Computational Harmonic Analysis, Volume 33 (2012) no. 1, p. 24 | DOI:10.1016/j.acha.2011.09.003
- Two are better than one: Fundamental parameters of frame coherence, Applied and Computational Harmonic Analysis, Volume 33 (2012) no. 1, p. 58 | DOI:10.1016/j.acha.2011.09.005
- Uncertainty Relations and Sparse Signal Recovery for Pairs of General Signal Sets, IEEE Transactions on Information Theory, Volume 58 (2012) no. 1, p. 263 | DOI:10.1109/tit.2011.2167215
- Least Squares Superposition Codes of Moderate Dictionary Size Are Reliable at Rates up to Capacity, IEEE Transactions on Information Theory, Volume 58 (2012) no. 5, p. 2541 | DOI:10.1109/tit.2012.2184847
- Invertibility of random submatrices via tail-decoupling and a matrix Chernoff inequality, Statistics Probability Letters, Volume 82 (2012) no. 7, p. 1479 | DOI:10.1016/j.spl.2012.03.038
- , 2010 44th Annual Conference on Information Sciences and Systems (CISS) (2010), p. 1 | DOI:10.1109/ciss.2010.5464824
- , 2010 48th Annual Allerton Conference on Communication, Control, and Computing (Allerton) (2010), p. 977 | DOI:10.1109/allerton.2010.5707015
- Beyond Nyquist: Efficient Sampling of Sparse Bandlimited Signals, IEEE Transactions on Information Theory, Volume 56 (2010) no. 1, p. 520 | DOI:10.1109/tit.2009.2034811
- Why Gabor frames? Two fundamental measures of coherence and their role in model selection, Journal of Communications and Networks, Volume 12 (2010) no. 4, p. 289 | DOI:10.1109/jcn.2010.6388466
- Computational Methods for Sparse Solution of Linear Inverse Problems, Proceedings of the IEEE, Volume 98 (2010) no. 6, p. 948 | DOI:10.1109/jproc.2010.2044010
- Compressive Sensing by Random Convolution, SIAM Journal on Imaging Sciences, Volume 2 (2009) no. 4, p. 1098 | DOI:10.1137/08072975x
- Near-ideal model selection by ℓ1 minimization, The Annals of Statistics, Volume 37 (2009) no. 5A | DOI:10.1214/08-aos653
Cité par 38 documents. Sources : Crossref
Commentaires - Politique
Vous devez vous connecter pour continuer.
S'authentifier