메뉴 건너뛰기




Volumn 17, Issue , 2016, Pages

Iterative Hessian sketch: Fast and accurate solution approximation for constrained least-squares

Author keywords

Convex optimization; Information theory; Lasso; Low rank approximation; Random projection

Indexed keywords

APPROXIMATION THEORY; CONVEX OPTIMIZATION; INFORMATION THEORY; ITERATIVE METHODS; PROBLEM SOLVING;

EID: 84974641899     PISSN: 15324435     EISSN: 15337928     Source Type: Journal    
DOI: None     Document Type: Article
Times cited : (206)

References (50)
  • 3
    • 55149088329 scopus 로고    scopus 로고
    • Convex multi-task feature learning
    • A. Argyriou, T. Evgeniou, and M. Pontil. Convex multi-task feature learning. Machine Learning, 73(3):243-272, 2008. ISSN 0885-6125. doi: 10.1007/s10994-007-5040-8. URL http://dx.doi.org/10.1007/s10994-007-5040-8.
    • (2008) Machine Learning , vol.73 , Issue.3 , pp. 243-272
    • Argyriou, A.1    Evgeniou, T.2    Pontil, M.3
  • 5
    • 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
  • 8
    • 85014561619 scopus 로고    scopus 로고
    • A fast iterative shrinkage-thresholding algorithm for linear inverse problems
    • A. Beck and M. Teboulle. A fast iterative shrinkage-thresholding algorithm for linear inverse problems. SIAM Journal on Imaging Sciences, 2(1):183-202, 2009.
    • (2009) SIAM Journal on Imaging Sciences , vol.2 , Issue.1 , pp. 183-202
    • Beck, A.1    Teboulle, M.2
  • 9
    • 0038582523 scopus 로고
    • Estimating a density under order restrictions: Non-asymptotic minimax risk
    • March
    • L. Birgé. Estimating a density under order restrictions: Non-asymptotic minimax risk. Annals of Statistics, 15(3):995-1012, March 1987.
    • (1987) Annals of Statistics , vol.15 , Issue.3 , pp. 995-1012
    • Birgé, L.1
  • 10
    • 84939568010 scopus 로고    scopus 로고
    • Toward a unified theory of sparse dimensionality reduction in euclidean space
    • J. Bourgain, S. Dirksen, and J. Nelson. Toward a unified theory of sparse dimensionality reduction in euclidean space. Geometric and Functional Analysis, 25(4), 2015.
    • (2015) Geometric and Functional Analysis , vol.25 , Issue.4
    • Bourgain, J.1    Dirksen, S.2    Nelson, J.3
  • 11
    • 67349198133 scopus 로고    scopus 로고
    • Random projections for the nonnegative least-squares problem
    • C. Boutsidis and P. Drineas. Random projections for the nonnegative least-squares problem. Linear Algebra and its Applications, 431(5-7):760-771, 2009.
    • (2009) Linear Algebra and Its Applications , vol.431 , Issue.5-7 , pp. 760-771
    • Boutsidis, C.1    Drineas, P.2
  • 12
    • 82655182661 scopus 로고    scopus 로고
    • Optimal selection of reduced rank estimators of high-dimensional matrices
    • F. Bunea, Y. She, and M. Wegkamp. Optimal selection of reduced rank estimators of high-dimensional matrices. Annals of Statistics, 39(2):1282-1309, 2011.
    • (2011) Annals of Statistics , vol.39 , Issue.2 , pp. 1282-1309
    • Bunea, F.1    She, Y.2    Wegkamp, M.3
  • 13
    • 29144439194 scopus 로고    scopus 로고
    • Decoding by linear programming
    • December
    • E. J. Candes and T. Tao. Decoding by linear programming. IEEE Trans. Info Theory, 51 (12):4203-4215, December 2005.
    • (2005) IEEE Trans. Info Theory , vol.51 , Issue.12 , pp. 4203-4215
    • Candes, E.J.1    Tao, T.2
  • 23
    • 35648994961 scopus 로고    scopus 로고
    • Gaussian averages of interpolated bodies and applications to approximate reconstruction
    • Y. Gordon, A. E. Litvak, S. Mendelson, and A. Pajor. Gaussian averages of interpolated bodies and applications to approximate reconstruction. Journal of Approximation Theory, 149:59-73, 2007.
    • (2007) Journal of Approximation Theory , vol.149 , pp. 59-73
    • Gordon, Y.1    Litvak, A.E.2    Mendelson, S.3    Pajor, A.4
  • 24
    • 0001033261 scopus 로고    scopus 로고
    • Robust regression: Asymptotics, conjectures and Monte Carlo
    • P. Huber. Robust regression: Asymptotics, conjectures and Monte Carlo. Annals of Statistics, 1:799-821, 2001.
    • (2001) Annals of Statistics , vol.1 , pp. 799-821
    • Huber, P.1
  • 25
    • 84893229593 scopus 로고    scopus 로고
    • Sparser Johnson-Lindenstrauss transforms
    • D. M. Kane and J. Nelson. Sparser Johnson-Lindenstrauss transforms. Journal of the ACM, 61(1), 2014.
    • (2014) Journal of the ACM , vol.61 , Issue.1
    • Kane, D.M.1    Nelson, J.2
  • 27
    • 84872078104 scopus 로고    scopus 로고
    • High-dimensional regression with noisy and missing data: Provable guarantees with non-convexity
    • September
    • P. Loh and M. J. Wainwright. High-dimensional regression with noisy and missing data: Provable guarantees with non-convexity. Annals of Statistics, 40(3):1637-1664, September 2012.
    • (2012) Annals of Statistics , vol.40 , Issue.3 , pp. 1637-1664
    • Loh, P.1    Wainwright, M.J.2
  • 31
    • 79952934740 scopus 로고    scopus 로고
    • Estimation of (near) low-rank matrices with noise and high-dimensional scaling
    • S. Negahban and M. J. Wainwright. Estimation of (near) low-rank matrices with noise and high-dimensional 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
  • 32
    • 84862020232 scopus 로고    scopus 로고
    • Restricted strong convexity and (weighted) matrix completion: Optimal bounds with noise
    • May
    • 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, May 2012.
    • (2012) Journal of Machine Learning Research , vol.13 , pp. 1665-1697
    • Negahban, S.1    Wainwright, M.J.2
  • 33
  • 35
    • 84939825294 scopus 로고    scopus 로고
    • Randomized sketches of convex programs with sharp guarantees
    • September
    • M. Pilanci and M. J. Wainwright. Randomized sketches of convex programs with sharp guarantees. IEEE Trans. Info. Theory, 9(61):5096-5115, September 2015a.
    • (2015) IEEE Trans. Info. Theory , vol.9 , Issue.61 , pp. 5096-5115
    • Pilanci, M.1    Wainwright, M.J.2
  • 39
    • 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
  • 40
    • 51649090940 scopus 로고    scopus 로고
    • A fast randomized algorithm for overdetermined linear least-squares regression
    • V. Rokhlin and M. Tygert. A fast randomized algorithm for overdetermined linear least-squares regression. Proceedings of the National Academy of Sciences, 105(36):13212-13217, 2008.
    • (2008) Proceedings of the National Academy of Sciences , vol.105 , Issue.36 , pp. 13212-13217
    • Rokhlin, V.1    Tygert, M.2
  • 42
    • 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
  • 46
    • 84863879353 scopus 로고    scopus 로고
    • Coordinate descent algorithms for Lasso penalized regression
    • T. T. Wu and K. Lange. Coordinate descent algorithms for Lasso penalized regression. Annals of Applied Statistics, 2(1):224-244, 2008.
    • (2008) Annals of Applied Statistics , vol.2 , Issue.1 , pp. 224-244
    • Wu, T.T.1    Lange, K.2
  • 49
    • 33645035051 scopus 로고    scopus 로고
    • Model selection and estimation in regression with grouped variables
    • M. Yuan and Y. Lin. Model selection and estimation in regression with grouped variables. Journal of the Royal Statistical Society B, 1(68):49, 2006.
    • (2006) Journal of the Royal Statistical Society B , vol.1 , Issue.68 , pp. 49
    • Yuan, M.1    Lin, Y.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.