메뉴 건너뛰기




Volumn 13, Issue , 2012, Pages 1665-1697

Restricted strong convexity and weighted matrix completion: Optimal bounds with noise

Author keywords

Collaborative filtering; Convex optimization; Matrix completion

Indexed keywords

COLLABORATIVE FILTERING; ERROR BOUND; FROBENIUS NORM; HIGH PROBABILITY; INFORMATION-THEORETIC METHODS; LOW-RANK MATRICES; M-ESTIMATORS; MATRIX COMPLETION; MATRIX COMPLETION PROBLEMS; NON-ASYMPTOTIC; OBSERVATION OPERATOR; OPTIMAL BOUNDS;

EID: 84862020232     PISSN: 15324435     EISSN: 15337928     Source Type: Journal    
DOI: None     Document Type: Article
Times cited : (479)

References (36)
  • 1
    • 84862017781 scopus 로고    scopus 로고
    • Noisy matrix decomposition via convex relaxation: Optimal rates in high dimensions
    • To appear
    • A. Agarwal, S. Negahban, and M. J. Wainwright. Noisy matrix decomposition via convex relaxation: Optimal rates in high dimensions. Annals of Statistics, 2011. To appear.
    • (2011) Annals of Statistics
    • Agarwal, A.1    Negahban, S.2    Wainwright, M.J.3
  • 2
    • 0036495139 scopus 로고    scopus 로고
    • Strong converse for identification via quantum channels
    • DOI 10.1109/18.985947, PII S0018944802010593
    • R. Ahlswede and A. Winter. Strong converse for identification via quantum channels. IEEE Transactions on Information Theory, 48(3):569-579, March 2002. (Pubitemid 34239788)
    • (2002) IEEE Transactions on Information Theory , vol.48 , Issue.3 , pp. 569-579
    • Ahlswede, R.1    Winter, A.2
  • 3
    • 46249124832 scopus 로고    scopus 로고
    • Consistency of trace norm minimization
    • June
    • F. Bach. Consistency of trace norm minimization. Journal of Machine Learning Research, 9:1019-1048, June 2008.
    • (2008) Journal of Machine Learning Research , vol.9 , pp. 1019-1048
    • Bach, F.1
  • 5
    • 77952741387 scopus 로고    scopus 로고
    • Matrix completion with noise
    • E. Candes and Y. Plan. Matrix completion with noise. Proceedings of the IEEE, 98(6):925-936, 2010.
    • (2010) Proceedings of the IEEE , vol.98 , Issue.6 , pp. 925-936
    • Candes, E.1    Plan, Y.2
  • 6
    • 71049116435 scopus 로고    scopus 로고
    • Exact matrix completion via convex optimization
    • E. J. Candes and B. Recht. Exact matrix completion via convex optimization. Found. Comput. Math., 9(6):717-772, 2009.
    • (2009) Found. Comput. Math. , vol.9 , Issue.6 , pp. 717-772
    • Candes, E.J.1    Recht, B.2
  • 7
    • 77951528523 scopus 로고    scopus 로고
    • The power of convex relaxation: Near-optimal matrix completion
    • E. J. Candes and T. Tao. The power of convex relaxation: Near-optimal matrix completion. IEEE Transactions on Information Theory, 56(5):2053-2080, 2010.
    • (2010) IEEE Transactions on Information Theory , vol.56 , Issue.5 , pp. 2053-2080
    • Candes, E.J.1    Tao, T.2
  • 8
    • 0012070851 scopus 로고    scopus 로고
    • Local operator theory, random matrices, and Banach spaces
    • Elsevier, Amsterdam, NL
    • K. R. Davidson and S. J. Szarek. Local operator theory, random matrices, and Banach spaces. In Handbook of Banach Spaces, volume 1, pages 317-336. Elsevier, Amsterdam, NL, 2001.
    • (2001) Handbook of Banach Spaces , vol.1 , pp. 317-336
    • Davidson, K.R.1    Szarek, S.J.2
  • 10
    • 0142257025 scopus 로고    scopus 로고
    • PhD thesis, Stanford, Available online
    • M. Fazel. Matrix Rank Minimization with Applications. PhD thesis, Stanford, 2002. Available online: http://faculty.washington. edu/mfazel/thesis-final.pdf.
    • (2002) Matrix Rank Minimization with Applications
    • Fazel, M.1
  • 11
    • 79951886985 scopus 로고    scopus 로고
    • Recovering low-rank matrices from few coefficients in any basis
    • March
    • D. Gross. Recovering low-rank matrices from few coefficients in any basis. IEEE Transactions on Information Theory, 57(3):1548-1566, March 2011.
    • (2011) IEEE Transactions on Information Theory , vol.57 , Issue.3 , pp. 1548-1566
    • Gross, D.1
  • 15
    • 3042743084 scopus 로고    scopus 로고
    • Matrix completion problems
    • Kluwer Academic
    • M. Laurent. Matrix completion problems. In The Encyclopedia of Optimization, pages 221-229. Kluwer Academic, 2001.
    • (2001) The Encyclopedia of Optimization , pp. 221-229
    • Laurent, M.1
  • 16
    • 0038609707 scopus 로고    scopus 로고
    • Mathematical Surveys and Monographs. American Mathematical Society, Providence, RI
    • M. Ledoux. The Concentration of Measure Phenomenon. Mathematical Surveys and Monographs. American Mathematical Society, Providence, RI, 2001.
    • (2001) The Concentration of Measure Phenomenon
    • Ledoux, M.1
  • 18
    • 77951134100 scopus 로고    scopus 로고
    • Fast convex optimization algorithms for exact recovery of a corrupted low-rank matrix
    • Univ. Illinois, Urbana-Champaign, July
    • Z. Lin, A. Ganesh, J. Wright, L. Wu, M. Chen, and Y. Ma. Fast convex optimization algorithms for exact recovery of a corrupted low-rank matrix. Technical Report UILU-ENG-09-2214, Univ. Illinois, Urbana-Champaign, July 2009.
    • (2009) Technical Report UILU-ENG-09-2214
    • Lin, Z.1    Ganesh, A.2    Wright, J.3    Wu, L.4    Chen, M.5    Ma, Y.6
  • 19
    • 77956944781 scopus 로고    scopus 로고
    • Spectral regularization algorithms for learning large incomplete matrices
    • August
    • R. Mazumber, T. Hastie, and R. Tibshirani. Spectral regularization algorithms for learning large incomplete matrices. Journal of Machine Learning Research, 11:2287-2322, August 2010.
    • (2010) Journal of Machine Learning Research , vol.11 , pp. 2287-2322
    • Mazumber, R.1    Hastie, T.2    Tibshirani, R.3
  • 20
    • 79952934740 scopus 로고    scopus 로고
    • Estimation of (near) low-rank matrices with noise and highdimensional scaling
    • S. Negahban and M. J. Wainwright. Estimation of (near) low-rank matrices with noise and highdimensional scaling. Annals of Statistics, 39(2):1069-1097, 2011.
    • (2011) Annals of Statistics , vol.39 , Issue.2 , pp. 1069-1097
    • Negahban, S.1    Wainwright, M.J.2
  • 21
    • 84858717588 scopus 로고    scopus 로고
    • A unified framework for highdimensional analysis of M-estimators with decomposable regularizers
    • Vancouver, Canada, December, To appear in Statistical Science
    • S. Negahban, P. Ravikumar, M. J. Wainwright, and B. Yu. A unified framework for highdimensional analysis of M-estimators with decomposable regularizers. In Neural Information Processing Systems (NIPS), Vancouver, Canada, December 2009. To appear in Statistical Science.
    • (2009) Neural Information Processing Systems (NIPS)
    • Negahban, S.1    Ravikumar, P.2    Wainwright, M.J.3    Yu, B.4
  • 24
    • 84856009825 scopus 로고    scopus 로고
    • A simpler approach to matrix completion
    • B. Recht. A simpler approach to matrix completion. Journal of Machine Learning Research, 12:3413-3430, 2011.
    • (2011) Journal of Machine Learning Research , vol.12 , pp. 3413-3430
    • Recht, B.1
  • 25
    • 78549288866 scopus 로고    scopus 로고
    • Guaranteed minimum-rank solutions of linear matrix equations via nuclear norm minimization
    • B. Recht, M. Fazel, and P. Parrilo. Guaranteed minimum-rank solutions of linear matrix equations via nuclear norm minimization. SIAM Review, 52(3):471-501, 2010.
    • (2010) SIAM Review , vol.52 , Issue.3 , pp. 471-501
    • Recht, B.1    Fazel, M.2    Parrilo, P.3
  • 26
    • 79952902758 scopus 로고    scopus 로고
    • Estimation of high-dimensional low-rank matrices
    • A. Rohde and A. Tsybakov. Estimation of high-dimensional low-rank matrices. Annals of Statistics, 39(2):887-930, 2011.
    • (2011) Annals of Statistics , vol.39 , Issue.2 , pp. 887-930
    • Rohde, A.1    Tsybakov, A.2
  • 27
    • 77956502973 scopus 로고    scopus 로고
    • Collaborative filtering in a non-uniform world: Learning with the weighted trace norm
    • Toyota Institute of Technology
    • R. Salakhutdinov and N. Srebro. Collaborative filtering in a non-uniform world: Learning with the weighted trace norm. Technical Report abs/1002.2780v1, Toyota Institute of Technology, 2010.
    • (2010) Technical Report abs/1002.2780v1
    • Salakhutdinov, R.1    Srebro, N.2
  • 30
    • 26944475424 scopus 로고    scopus 로고
    • Generalization error bounds for collaborative prediction with low-rank matrices
    • Vancouver, Canada, December
    • N. Srebro, N. Alon, and T. S. Jaakkola. Generalization error bounds for collaborative prediction with low-rank matrices. In Neural Information Processing Systems (NIPS), Vancouver, Canada, December 2005.
    • (2005) Neural Information Processing Systems (NIPS)
    • Srebro, N.1    Alon, N.2    Jaakkola, T.S.3
  • 31
    • 0012913015 scopus 로고
    • The finite dimensional basis problem with an appendix on nets of grassmann manifolds
    • S. J. Szarek. The finite dimensional basis problem with an appendix on nets of grassmann manifolds. Acta Mathematica, 151:153-179, 1983.
    • (1983) Acta Mathematica , vol.151 , pp. 153-179
    • Szarek, S.J.1
  • 32
    • 79551520865 scopus 로고    scopus 로고
    • User-friendly tail bounds for matrix martingales
    • April
    • J. Tropp. User-friendly tail bounds for matrix martingales. Technical report, Caltech, April 2010.
    • (2010) Technical Report, Caltech
    • Tropp, J.1
  • 33
    • 84862017782 scopus 로고    scopus 로고
    • A note on sums of independent random matrices after Ahlswede-Winter
    • Univ. Michigan, December
    • R. Vershynin. A note on sums of independent random matrices after Ahlswede-Winter. Technical report, Univ. Michigan, December 2009.
    • (2009) Technical Report
    • Vershynin, R.1
  • 34
    • 84857918539 scopus 로고    scopus 로고
    • Introduction to the non-asymptotic analysis of random matrices
    • R. Vershynin. Introduction to the non-asymptotic analysis of random matrices. Compressed Sensing: Theory and Applications, 2012. Available at http://www-personal.umich.edu/~romanv/papers/non-asymptotic-rmt-plain.pdf.
    • (2012) Compressed Sensing: Theory and Applications
    • Vershynin, R.1
  • 35
    • 0033233737 scopus 로고    scopus 로고
    • Information-theoretic determination of minimax rates of convergence
    • Y. Yang and A. Barron. Information-theoretic determination of minimax rates of convergence. Annals of Statistics, 27(5):1564-1599, 1999.
    • (1999) Annals of Statistics , vol.27 , Issue.5 , pp. 1564-1599
    • Yang, Y.1    Barron, A.2
  • 36
    • 17644388356 scopus 로고    scopus 로고
    • Assouad, fano and le cam
    • Springer-Verlag, Berlin
    • B. Yu. Assouad, Fano and Le Cam. In Festschrift for Lucien Le Cam, pages 423-435. Springer-Verlag, Berlin, 1997.
    • (1997) Festschrift for Lucien le Cam , pp. 423-435
    • Yu, B.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.