메뉴 건너뛰기




Volumn 42, Issue 6, 2014, Pages 2413-2440

Minimax risk of matrix denoising by singular value thresholding

Author keywords

Matrix completion from Gaussian measurements; Matrix denoising; Monotonicity of power functions of multivariate tests; Nuclear norm minimization; Optimal threshold; Phase transition; Singular value thresholding; Stein unbiased risk estimate

Indexed keywords


EID: 84908192014     PISSN: 00905364     EISSN: 21688966     Source Type: Journal    
DOI: 10.1214/14-AOS1257     Document Type: Article
Times cited : (112)

References (25)
  • 1
    • 84968476146 scopus 로고
    • The integral of a symmetric unimodal function over a symmetric convex set and some probability inequalities
    • MR0069229
    • ANDERSON, T. W. (1955). The integral of a symmetric unimodal function over a symmetric convex set and some probability inequalities. Proc. Amer. Math. Soc. 6 170-176. MR0069229
    • (1955) Proc. Amer. Math. Soc. , vol.6 , pp. 170-176
    • Anderson, T.W.1
  • 2
    • 84883334291 scopus 로고    scopus 로고
    • Unbiased risk estimates for singular value thresholding and spectral estimators
    • MR3105401
    • CANDÈS, E. J., SING-LONG, C. A. and TRZASKO, J. D. (2013). Unbiased risk estimates for singular value thresholding and spectral estimators. IEEE Trans. Signal Process. 61 4643-4657. MR3105401
    • (2013) IEEE Trans. Signal Process. , vol.61 , pp. 4643-4657
    • Candès, E.J.1    Sing-Long, C.A.2    Trzasko, J.D.3
  • 3
    • 0005464932 scopus 로고
    • Monotonicity of the power functions of some tests of the multivariate linear hypothesis
    • MR0158474
    • DAS GUPTA, S., ANDERSON, T. W. and MUDHOLKAR, G. S. (1964). Monotonicity of the power functions of some tests of the multivariate linear hypothesis. Ann. Math. Statist. 35 200-205. MR0158474
    • (1964) Ann. Math. Statist. , vol.35 , pp. 200-205
    • Das Gupta, S.1    Anderson, T.W.2    Mudholkar, G.S.3
  • 6
    • 84878157685 scopus 로고    scopus 로고
    • The phase transition of matrix recovery from Gaussian measurements matches the minimax MSE of matrix denoising
    • MR3082268
    • DONOHO, D. L., GAVISH, M. and MONTANARI, A. (2013). The phase transition of matrix recovery from Gaussian measurements matches the minimax MSE of matrix denoising. Proc. Natl. Acad. Sci. USA 110 8405-8410. MR3082268
    • (2013) Proc. Natl. Acad. Sci. USA , vol.110 , pp. 8405-8410
    • Donoho, D.L.1    Gavish, M.2    Montanari, A.3
  • 7
    • 84877914996 scopus 로고    scopus 로고
    • Accurate Prediction of Phase Transitions in Compressed Sensing Via A Connection to Minimax Denoising
    • MR3061255
    • DONOHO, D. L., JOHNSTONE, I. and MONTANARI, A. (2013). Accurate prediction of phase transitions in compressed sensing via a connection to minimax denoising. IEEE Trans. Inform. Theory 59 3396-3433. MR3061255
    • (2013) IEEE Trans. Inform. Theory , vol.59 , pp. 3396-3433
    • Donoho, D.L.1    Johnstone, I.2    Montanari, A.3
  • 10
    • 84904607493 scopus 로고    scopus 로고
    • The optimal hard threshold for singular values is 4/V3
    • GAVISH, M. and DONOHO, D. L. (2014). The optimal hard threshold for singular values is 4/V3. IEEE Trans. Inform. Theory 60 5040-5053.
    • (2014) IEEE Trans. Inform. Theory , vol.60 , pp. 5040-5053
    • Gavish, M.1    Donoho, D.L.2
  • 12
    • 82655171609 scopus 로고    scopus 로고
    • Nuclear-norm penalization and optimal rates for noisy low-rank matrix completion
    • MR2906869
    • KOLTCHINSKII, V., LOUNICI, K. and TSYBAKOV, A. B. (2011). Nuclear-norm penalization and optimal rates for noisy low-rank matrix completion. Ann. Statist. 39 2302-2329. MR2906869
    • (2011) Ann. Statist. , vol.39 , pp. 2302-2329
    • Koltchinskii, V.1    Lounici, K.2    Tsybakov, A.B.3
  • 13
    • 0039119760 scopus 로고
    • The convex analysis of unitarily invariant matrix functions
    • MR1363368
    • LEWIS, A. S. (1995). The convex analysis of unitarily invariant matrix functions. J. Convex Anal. 2 173-183. MR1363368
    • (1995) J. Convex Anal. , vol.2 , pp. 173-183
    • Lewis, A.S.1
  • 14
    • 22044456250 scopus 로고    scopus 로고
    • Nonsmooth analysis of singular values. i
    • MR2162512
    • LEWIS, A. S. and SENDOV, H. S. (2005). Nonsmooth analysis of singular values. I. Theory. Set-Valued Var. Anal. 13 213-241. MR2162512
    • (2005) Theory. Set-Valued Var. Anal. , vol.13 , pp. 213-241
    • Lewis, A.S.1    Sendov, H.S.2
  • 15
    • 0000263234 scopus 로고
    • Distribution of eigenvalues for some sets of random matrices
    • MARCENKO, V. and PASTUR, L. (1967). Distribution of eigenvalues for some sets of random matrices. Mathematics USSR Sbornik 1 457-483.
    • (1967) Mathematics USSR Sbornik , vol.1 , pp. 457-483
    • Marcenko, V.1    Pastur, L.2
  • 17
    • 84875754742 scopus 로고    scopus 로고
    • On a relation between the minimax risk and the phase transitions of compressed recovery
    • IEEE, Piscataway, NJ. Available at
    • OYMAK, S. and HASSIBI, B. (2012). On a relation between the minimax risk and the phase transitions of compressed recovery. In 2012 50th Annual Allerton Conference on Communication, Control, and Computing 1018-1025. IEEE, Piscataway, NJ. Available at http://ieeexplore.ieee.org/stamp/stamp.jsp?arnumber=6483330.
    • (2012) 2012 50th Annual Allerton Conference on Communication, Control, and Computing , pp. 1018-1025
    • Oymak, S.1    Hassibi, B.2
  • 18
    • 78549288866 scopus 로고    scopus 로고
    • Guaranteed minimum-rank solutions of linear matrix equations via nuclear norm minimization
    • MR2680543
    • RECHT, B., FAZEL, M. and PARRILO, P. A. (2010). Guaranteed minimum-rank solutions of linear matrix equations via nuclear norm minimization. SIAM Rev. 52 471-501. MR2680543
    • (2010) SIAM Rev. , vol.52 , pp. 471-501
    • Recht, B.1    Fazel, M.2    Parrilo, P.A.3
  • 20
    • 79952759680 scopus 로고    scopus 로고
    • Null space conditions and thresholds for rank minimization
    • MR2776714
    • RECHT, B., XU, W. and HASSIBI, B. (2011). Null space conditions and thresholds for rank minimization. Math. Program. 127 175-202. MR2776714
    • (2011) Math. Program. , vol.127 , pp. 175-202
    • Recht, B.1    Xu, W.2    Hassibi, B.3
  • 21
    • 79952902758 scopus 로고    scopus 로고
    • Estimation of high-dimensional low-rank matrices
    • MR2816342
    • ROHDE, A. and TSYBAKOV, A. B. (2011). Estimation of high-dimensional low-rank matrices. Ann. Statist. 39 887-930. MR2816342
    • (2011) Ann. Statist. , vol.39 , pp. 887-930
    • Rohde, A.1    Tsybakov, A.B.2
  • 23
    • 0000169918 scopus 로고
    • Estimation of the mean of a multivariate normal distribution
    • MR0630098
    • STEIN, C. M. (1981). Estimation of the mean of a multivariate normal distribution. Ann. Statist. 9 1135-1151. MR0630098
    • (1981) Ann. Statist. , vol.9 , pp. 1135-1151
    • Stein, C.M.1
  • 25
    • 65649136568 scopus 로고    scopus 로고
    • On the marginal distribution of the eigenvalues of Wishart matrices
    • ZANELLA, A., CHIANI, M. and WIN, M. Z. (2009). On the marginal distribution of the eigenvalues of Wishart matrices. IEEE Transactions on Communications 57 1050-1060.
    • (2009) IEEE Transactions on Communications , vol.57 , pp. 1050-1060
    • Zanella, A.1    Chiani, M.2    Win, M.Z.3


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.