메뉴 건너뛰기




Volumn 9, Issue , 2008, Pages 2287-2320

Randomized online PCA algorithms with regret bounds that are logarithmic in the dimension

Author keywords

Density matrix; Expert setting; Online learning; Principal component analysis; Quantum Bayes rule

Indexed keywords

A DENSITIES; BATCH ALGORITHMS; DENSITY MATRIX; EIGENVALUES; EXPERT SETTING; LOW DIMENSIONAL; ON-LINE LEARNINGS; ONLINE ALGORITHMS; ONLINE LEARNING; PCA ALGORITHMS; PRINCIPAL COMPONENTS; QUANTUM BAYES RULE; RUNNING TIMES; SUB SPACES;

EID: 56349165656     PISSN: 15324435     EISSN: 15337928     Source Type: Journal    
DOI: None     Document Type: Article
Times cited : (144)

References (38)
  • 1
    • 0035370926 scopus 로고    scopus 로고
    • K. Azoury and M. K. Warmuth. Relative loss bounds for on-line density estimation with the exponential family of distributions. Journal of Machine Learning, 43(3):211-246, June 2001. Special issue on Theoretical Advances in On-line Learning, Game Theory and Boosting, edited by Yoram Singer.
    • K. Azoury and M. K. Warmuth. Relative loss bounds for on-line density estimation with the exponential family of distributions. Journal of Machine Learning, 43(3):211-246, June 2001. Special issue on Theoretical Advances in On-line Learning, Game Theory and Boosting, edited by Yoram Singer.
  • 5
    • 49949144765 scopus 로고
    • The relaxation method of finding the common point of convex sets and its application to the solution of problems in convex programming
    • L. M. Bregman. The relaxation method of finding the common point of convex sets and its application to the solution of problems in convex programming. USSR Computational Mathematics and Physics, 7:200-217, 1967.
    • (1967) USSR Computational Mathematics and Physics , vol.7 , pp. 200-217
    • Bregman, L.M.1
  • 6
    • 0019587748 scopus 로고
    • An iterative row-action method for interval convex programming
    • July
    • Y. Censor and A. Lent. An iterative row-action method for interval convex programming. Journal of Optimization Theory and Applications, 34(3):321-353, July 1981.
    • (1981) Journal of Optimization Theory and Applications , vol.34 , Issue.3 , pp. 321-353
    • Censor, Y.1    Lent, A.2
  • 7
    • 84864029740 scopus 로고    scopus 로고
    • Improved risk tail bounds for on-line algorithms
    • N. Cesa-Bianchi and C. Gentile. Improved risk tail bounds for on-line algorithms. In NIPS, 2005.
    • (2005) NIPS
    • Cesa-Bianchi, N.1    Gentile, C.2
  • 11
    • 0031211090 scopus 로고    scopus 로고
    • A decision-theoretic generalization of on-line learning and an application to Boosting
    • August
    • Y Freund and R. E. Schapire. A decision-theoretic generalization of on-line learning and an application to Boosting. Journal of Computer and System Sciences, 55(1):119-139, August 1997.
    • (1997) Journal of Computer and System Sciences , vol.55 , Issue.1 , pp. 119-139
    • Freund, Y.1    Schapire, R.E.2
  • 12
    • 21844525426 scopus 로고
    • A stable and efficient algorithm for the rank-one modification of the symmetric eigenproblem
    • October
    • M. Gu and S. Eisenstat. A stable and efficient algorithm for the rank-one modification of the symmetric eigenproblem. SIAM Journal on Matrix Analysis and Applications, 15(4): 1266-1276, October 1994.
    • (1994) SIAM Journal on Matrix Analysis and Applications , vol.15 , Issue.4 , pp. 1266-1276
    • Gu, M.1    Eisenstat, S.2
  • 16
    • 0032137328 scopus 로고
    • Tracking the best expert
    • Earlier version in 12th ICML
    • M. Herbster and M. K. Warmuth. Tracking the best expert. Machine Learning, 32(2): 151-178, 1998. Earlier version in 12th ICML, 1995.
    • (1995) Machine Learning , vol.32 , Issue.2 , pp. 151-178
    • Herbster, M.1    Warmuth, M.K.2
  • 18
    • 56349133512 scopus 로고    scopus 로고
    • Simulating weighted majority with FPL. Private communication
    • A. Kalai. Simulating weighted majority with FPL. Private communication, 2005.
    • (2005)
    • Kalai, A.1
  • 19
    • 85128125736 scopus 로고    scopus 로고
    • A. Kalai and S. Vempala. Efficient algorithms for online decision problems. J. Comput. Syst. Sci., 71(3):291-307, 2005. Special issue Learning Theory 2003.
    • A. Kalai and S. Vempala. Efficient algorithms for online decision problems. J. Comput. Syst. Sci., 71(3):291-307, 2005. Special issue Learning Theory 2003.
  • 21
    • 0008815681 scopus 로고    scopus 로고
    • Additive versus exponentiated gradient updates for linear prediction
    • January
    • J. Kivinen and M. K. Warmuth. Additive versus exponentiated gradient updates for linear prediction. Information and Computation, 132(1): 1-64, January 1997.
    • (1997) Information and Computation , vol.132 , Issue.1 , pp. 1-64
    • Kivinen, J.1    Warmuth, M.K.2
  • 22
    • 0035575628 scopus 로고    scopus 로고
    • Relative loss bounds for multidimensional regression problems
    • J. Kivinen and M. K. Warmuth. Relative loss bounds for multidimensional regression problems. Machine Learning, 45(3):301-329, 2001.
    • (2001) Machine Learning , vol.45 , Issue.3 , pp. 301-329
    • Kivinen, J.1    Warmuth, M.K.2
  • 27
    • 35148838877 scopus 로고
    • The weighted majority algorithm
    • Preliminary version in in FOCS 89
    • N. Littlestone and M. K. Warmuth. The weighted majority algorithm. Inform. Comput., 108(2): 212-261, 1994. Preliminary version in in FOCS 89.
    • (1994) Inform. Comput , vol.108 , Issue.2 , pp. 212-261
    • Littlestone, N.1    Warmuth, M.K.2
  • 30
    • 0024883243 scopus 로고
    • Optimal unsupervised learning in a single-layer linear feedforward neural network
    • T. D. Sanger. Optimal unsupervised learning in a single-layer linear feedforward neural network. Neural Networks, 2:459-473, 1989.
    • (1989) Neural Networks , vol.2 , pp. 459-473
    • Sanger, T.D.1
  • 31
    • 22844440983 scopus 로고    scopus 로고
    • On the eigenspectrum of the gram matrix and the generalization error of kernel-PCA
    • URL
    • J. Shawe-Taylor, C. K. I. Williams, N. Cristianini, and J. S. Kandola. On the eigenspectrum of the gram matrix and the generalization error of kernel-PCA. IEEE Transactions on Information Theory, 51(7):2510-2522, 2005. URL http://dx.doi.org/10.1109/TIT.2005.850052.
    • (2005) IEEE Transactions on Information Theory , vol.51 , Issue.7 , pp. 2510-2522
    • Shawe-Taylor, J.1    Williams, C.K.I.2    Cristianini, N.3    Kandola, J.S.4
  • 33
    • 21844471282 scopus 로고    scopus 로고
    • Matrix exponentiated gradient updates for on-line learning and Bregman projections
    • June
    • K. Tsuda, G. Ratsch, and M. K. Warmuth. Matrix exponentiated gradient updates for on-line learning and Bregman projections. Journal of Machine Learning Research, 6:995-1018, June 2005.
    • (2005) Journal of Machine Learning Research , vol.6 , pp. 995-1018
    • Tsuda, K.1    Ratsch, G.2    Warmuth, M.K.3
  • 34
    • 56349166958 scopus 로고    scopus 로고
    • The blessing and the curse of the multiplicative updates. Work in progress
    • unpublished manuscript
    • M. K. Warmuth. The blessing and the curse of the multiplicative updates. Work in progress, unpublished manuscript., 2007a.
    • (2007)
    • Warmuth, M.K.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.