메뉴 건너뛰기




Volumn 14, Issue , 2013, Pages 3619-3647

A max-norm constrained minimization approach to 1-bit matrix completion

Author keywords

1 bit matrix completion; Constrained optimization; Low rank matrix; Max norm; Maximum likelihood estimate; Optimal rate of convergence; Trace norm

Indexed keywords

LOW-RANK MATRICES; MATRIX COMPLETION; MAX-NORM; MAXIMUM LIKELIHOOD ESTIMATE; OPTIMAL RATE OF CONVERGENCE; TRACE-NORM;

EID: 84893492266     PISSN: 15324435     EISSN: 15337928     Source Type: Journal    
DOI: None     Document Type: Article
Times cited : (153)

References (36)
  • 2
    • 0038453192 scopus 로고    scopus 로고
    • Rademacher and gaussian complexities: Risk bounds and structural results
    • P. Bartlett and S. Mendelson. Rademacher and Gaussian complexities: risk bounds and structural results. Journal of Machine Learning Research, 3:463-482, 2002.
    • (2002) Journal of Machine Learning Research , vol.3 , pp. 463-482
    • Bartlett, P.1    Mendelson, S.2
  • 3
    • 33746874045 scopus 로고    scopus 로고
    • Semidefinite programming based algorithms for sensor network localization
    • DOI 10.1145/1149283.1149286
    • P. Biswas, T. C. Lian, T. C.Wang and Y. Ye. Semidefinite programming based algorithms for sensor network localization. ACM Transactions on Sensor Networks, 2(2):188-220, 2006. (Pubitemid 44188494)
    • (2006) ACM Transactions on Sensor Networks , vol.2 , Issue.2 , pp. 188-220
    • Biswas, P.1    Lian, T.-C.2    Wang, T.-C.3    Ye, Y.4
  • 5
    • 1542337156 scopus 로고    scopus 로고
    • A nonlinear programming algorithm for solving semidefinite programs via low-rank factorization
    • DOI 10.1007/s10107-002-0352-8
    • S. Burer and R. D. C. Monteiro. A nonlinear programming algorithm for solving semidefinite programs via low-rank factorization. Mathematical Programming, Series B, 95(2):329-357, February 2003. (Pubitemid 44757858)
    • (2003) Mathematical Programming, Series B , vol.95 , Issue.2 , pp. 329-357
    • Burer, S.1    Monteiro, R.D.C.2
  • 10
    • 84893503709 scopus 로고    scopus 로고
    • Concentration-based guarantees for low-rank matrix reconstruction
    • R. Foygel and N. Srebro. Concentration-based guarantees for low-rank matrix reconstruction. JMLR: Workshop and Conference Proceedings, 19:315-339, 2011.
    • (2011) JMLR: Workshop and Conference Proceedings , vol.19 , pp. 315-339
    • Foygel, R.1    Srebro, N.2
  • 11
    • 84976668719 scopus 로고
    • Using collaborative filtering to weave an information tapestry
    • December
    • D. Goldberg, D. Nichols, B. M. Oki and D. Terry. Using collaborative filtering to weave an information tapestry. Communications of the ACM, 35(12):61-70, December 1992.
    • (1992) Communications of the ACM , vol.35 , Issue.12 , pp. 61-70
    • Goldberg, D.1    Nichols, D.2    Oki, B.M.3    Terry, D.4
  • 15
    • 84897524603 scopus 로고    scopus 로고
    • Revisiting frank-wolfe: Projection-free sparse convex optimization
    • M. Jaggi. Revisiting Frank-Wolfe: projection-free sparse convex optimization. JMLR: Workshop and Conference Proceedings, 28(1):427-435, 2013.
    • (2013) JMLR: Workshop and Conference Proceedings , vol.28 , Issue.1 , pp. 427-435
    • Jaggi, M.1
  • 16
    • 0039112124 scopus 로고
    • Summing and nuclear norms in banach space theory
    • Cambridge University Press, Cambridge
    • G. J. O. Jameson. Summing and Nuclear Norms in Banach Space Theory. London Mathematical Society Student Texts, 8. Cambridge University Press, Cambridge, 1987.
    • (1987) London Mathematical Society Student Texts , vol.8
    • Jameson, G.J.O.1
  • 17
    • 0000709793 scopus 로고
    • Negative association of random variables with applications
    • K. Joag-Dev and F. Proschan. Negative association of random variables with applications. Annals of Statistics, 11(1):286-295, 1983.
    • (1983) Annals of Statistics , vol.11 , Issue.1 , pp. 286-295
    • Joag-Dev, K.1    Proschan, F.2
  • 19
    • 82655171609 scopus 로고    scopus 로고
    • Nuclear norm penalization and optimal rates for noisy low rank matrix completion
    • V. Koltchinskii, K. Lounici and A. B. Tsybakov. Nuclear norm penalization and optimal rates for noisy low rank matrix completion. Annals of Statistics, 39(5):2302-2329, 2011.
    • (2011) Annals of Statistics , vol.39 , Issue.5 , pp. 2302-2329
    • Koltchinskii, V.1    Lounici, K.2    Tsybakov, A.B.3
  • 20
    • 84862605117 scopus 로고    scopus 로고
    • Regime change: Bit-depth versus measurement-rate in compressive sensing
    • J. N. Laska and R. G. Baraniuk. Regime change: bit-depth versus measurement-rate in compressive sensing. IEEE Transactions on Signal Processing, 60(7):3496-3505, 2012.
    • (2012) IEEE Transactions on Signal Processing , vol.60 , Issue.7 , pp. 3496-3505
    • Laska, J.N.1    Baraniuk, R.G.2
  • 21
    • 18144366601 scopus 로고    scopus 로고
    • Some estimates of norms of random matrices
    • DOI 10.1090/S0002-9939-04-07800-1, PII S0002993904078001
    • R. Latala. Some estimates of norms of random matrices. Proceedings of the AmericanMathematical Society, 133(5):1273-1282, 2005. (Pubitemid 40622652)
    • (2005) Proceedings of the American Mathematical Society , vol.133 , Issue.5 , pp. 1273-1282
    • Latala, R.1
  • 25
    • 84862020232 scopus 로고    scopus 로고
    • Restricted strong convexity and weighted matrix completion: Optimal bounds with noise
    • S. Negahban and M. J. Wainwright. Restricted strong convexity and weighted matrix completion: optimal bounds with noise. Journal of Machine Learning Research, 13:1665-1697, 2012.
    • (2012) Journal of Machine Learning Research , vol.13 , pp. 1665-1697
    • Negahban, S.1    Wainwright, M.J.2
  • 26
    • 84871749706 scopus 로고    scopus 로고
    • Robust 1-bit compressed sensing and sparse logistic regression: A convex programming approach
    • January
    • Y. Plan and R. Vershynin. Robust 1-bit compressed sensing and sparse logistic regression: a convex programming approach. IEEE Transactions on Information Theory, 59(1):482-494, January, 2013a.
    • (2013) IEEE Transactions on Information Theory , vol.59 , Issue.1 , pp. 482-494
    • Plan, Y.1    Vershynin, R.2
  • 29
    • 0034382620 scopus 로고    scopus 로고
    • The expected norm of random matrices
    • March
    • Y. Seginer. The expected norm of random matrices. Combinatorics, Probability and Computing, 9(2):149-166, March, 2000.
    • (2000) Combinatorics Probability and Computing , vol.9 , Issue.2 , pp. 149-166
    • Seginer, Y.1
  • 30
    • 0005520987 scopus 로고
    • Single subject incomplete designs for nonmetric multidimensional scaling
    • December
    • I. Spence and D. W. Domoney. Single subject incomplete designs for nonmetric multidimensional scaling. Psychometrika, 39(4):469-490, December, 1974.
    • (1974) Psychometrika , vol.39 , Issue.4 , pp. 469-490
    • Spence, I.1    Domoney, D.W.2
  • 34
    • 84864315555 scopus 로고    scopus 로고
    • User-friendly tail bounds for sums of random matrices
    • August
    • J. A. Tropp. User-friendly tail bounds for sums of random matrices. Foundations of Computational Mathematics, 12(4):389-434, August, 2012.
    • (2012) Foundations of Computational Mathematics , vol.12 , Issue.4 , pp. 389-434
    • Tropp, J.A.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


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.