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Volumn 10, Issue 3-4, 2017, Pages 142-336

Non-convex optimization for machine learning

Author keywords

[No Author keywords available]

Indexed keywords

ARTIFICIAL INTELLIGENCE; CONVEX OPTIMIZATION; FUNCTIONS; HEURISTIC METHODS; INFERENCE ENGINES; LEARNING ALGORITHMS; LEARNING SYSTEMS; PROBLEM SOLVING;

EID: 85037538890     PISSN: 19358237     EISSN: 19358245     Source Type: Journal    
DOI: 10.1561/2200000058     Document Type: Article
Times cited : (472)

References (132)
  • 1
    • 84873371070 scopus 로고    scopus 로고
    • Fast global convergence of gradient methods for high-dimensional statistical recovery
    • Alekh Agarwal, Sahand N. Negahban, and Martin J. Wainwright. Fast global convergence of gradient methods for high-dimensional statistical recovery. The Annals of Statistics, 40(5):2452-2482, 2012.
    • (2012) The Annals of Statistics , vol.40 , Issue.5 , pp. 2452-2482
    • Agarwal, A.1    Negahban, S.N.2    Wainwright, M.J.3
  • 2
    • 85007153684 scopus 로고    scopus 로고
    • Learning sparsely used overcomplete dictionaries via alternating minimization
    • Alekh Agarwal, Animashree Anandkumar, Prateek Jain, and Praneeth Netrapalli. Learning Sparsely Used Overcomplete Dictionaries via Alternating Minimization. SIAM Journal of Optimization, 26(4):2775-2799, 2016.
    • (2016) SIAM Journal of Optimization , vol.26 , Issue.4 , pp. 2775-2799
    • Agarwal, A.1    Anandkumar, A.2    Jain, P.3    Netrapalli, P.4
  • 4
    • 85072254591 scopus 로고    scopus 로고
    • Efficient approaches for escaping higher order saddle points in non-convex optimization
    • Animashree Anandkumar and Rong Ge. Efficient approaches for escaping higher order saddle points in non-convex optimization. In Proceedings of the 29th Conference on Learning Theory (COLT), pages 81-102, 2016.
    • (2016) Proceedings of the 29th Conference on Learning Theory (COLT) , pp. 81-102
    • Anandkumar, A.1    Ge, R.2
  • 9
    • 85015063414 scopus 로고    scopus 로고
    • Statistical guarantees for the EM algorithm: From population to sample-based analysis
    • Sivaraman Balakrishnan, Martin J. Wainwright, and Bin Yu. Statistical Guarantees for the EM Algorithm: From Population to Sample-based Analysis. Annals of Statistics, 45(1):77-120, 2017.
    • (2017) Annals of Statistics , vol.45 , Issue.1 , pp. 77-120
    • Balakrishnan, S.1    Wainwright, M.J.2    Yu, B.3
  • 10
    • 55649115527 scopus 로고    scopus 로고
    • A simple proof of the restricted isometry property for random matrices
    • Richard Baraniuk, Mark Davenport, Ronald DeVore, and Michael Wakin. A Simple Proof of the Restricted Isometry Property for Random Matrices. Constructive Approximation, 28(3):253-263, 2008.
    • (2008) Constructive Approximation , vol.28 , Issue.3 , pp. 253-263
    • Baraniuk, R.1    Davenport, M.2    DeVore, R.3    Wakin, M.4
  • 15
    • 79959569827 scopus 로고    scopus 로고
    • Sampling and reconstructing signals from a union of linear subspaces
    • Thomas Blumensath. Sampling and Reconstructing Signals From a Union of Linear Subspaces. IEEE Transactions on Information Theory, 57(7): 4660-4671, 2011.
    • (2011) IEEE Transactions on Information Theory , vol.57 , Issue.7 , pp. 4660-4671
    • Blumensath, T.1
  • 19
    • 84983143287 scopus 로고    scopus 로고
    • Convex optimization: Algorithms and complexity
    • Sebastien Bubeck. Convex Optimization: Algorithms and Complexity. Foundations and Trends® in Machine Learning, 8(34):231-357, 2015.
    • (2015) Foundations and Trends® in Machine Learning , vol.8 , Issue.34 , pp. 231-357
    • Bubeck, S.1
  • 20
    • 77951291046 scopus 로고    scopus 로고
    • A singular value thresholding algorithm for matrix completion
    • Jian-Feng Cai, Emmanuel J. Candès, and Zuowei Shen. A Singular Value Thresholding Algorithm for Matrix Completion. SIAM Journal of Optimization, 20(4):1956-1982, 2010.
    • (2010) SIAM Journal of Optimization , vol.20 , Issue.4 , pp. 1956-1982
    • Cai, J.-F.1    Candès, E.J.2    Shen, Z.3
  • 22
    • 42649140570 scopus 로고    scopus 로고
    • The restricted isometry property and its implications for compressed sensing
    • Emmanuel J. Candès. The Restricted Isometry Property and Its Implications for Compressed Sensing. Comptes Rendus Mathematique, 346(9-10):589-592, 2008.
    • (2008) Comptes Rendus Mathematique , vol.346 , Issue.9-10 , pp. 589-592
    • Candès, E.J.1
  • 23
    • 84919976187 scopus 로고    scopus 로고
    • Solving quadratic equations via PhaseLift when there are about as many equations as unknowns
    • Emmanuel J. Candès and Xiaodong Li. Solving Quadratic Equations via PhaseLift When There Are About as Many Equations as Unknowns. Foundations of Computational Mathematics, 14(5):1017-1026, 2014.
    • (2014) Foundations of Computational Mathematics , vol.14 , Issue.5 , pp. 1017-1026
    • Candès, E.J.1    Li, X.2
  • 24
    • 71049116435 scopus 로고    scopus 로고
    • Exact matrix completion via convex optimization
    • Emmanuel J. Candès and Benjamin Recht. Exact Matrix Completion via Convex Optimization. Foundations of Computational Mathematics, 9(6): 717-772, 2009.
    • (2009) Foundations of Computational Mathematics , vol.9 , Issue.6 , pp. 717-772
    • Candès, E.J.1    Recht, B.2
  • 25
    • 77951528523 scopus 로고    scopus 로고
    • The power of convex relaxation: Near-optimal matrix completion
    • Emmanuel J. Candès and Terence Tao. The power of convex relaxation: Near-optimal matrix completion. IEEE Transactions on Information Theory, 56 (5):2053-2080, 2009.
    • (2009) IEEE Transactions on Information Theory , vol.56 , Issue.5 , pp. 2053-2080
    • Candès, E.J.1    Tao, T.2
  • 26
    • 33745604236 scopus 로고    scopus 로고
    • Stable signal recovery from incomplete and inaccurate measurements
    • Emmanuel J. Candès, Justin K. Romberg, and Terence Tao. Stable Signal Recovery from Incomplete and Inaccurate Measurements. Communications on Pure and Applied Mathematics, 59(8):1207-1223, 2006.
    • (2006) Communications on Pure and Applied Mathematics , vol.59 , Issue.8 , pp. 1207-1223
    • Candès, E.J.1    Romberg, J.K.2    Tao, T.3
  • 29
    • 34548724437 scopus 로고    scopus 로고
    • Exact reconstruction of sparse signals via nonconvex minimization
    • Rick Chartrand. Exact Reconstruction of Sparse Signals via Nonconvex Minimization. IEEE Information Processing Letters, 14(10):707-710, 2007.
    • (2007) IEEE Information Processing Letters , vol.14 , Issue.10 , pp. 707-710
    • Chartrand, R.1
  • 30
    • 84863068818 scopus 로고    scopus 로고
    • Matrix completion via an alternating direction method
    • Caihua Chen and Bingsheng He. Matrix Completion via an Alternating Direction Method. IMA Journal of Numerical Analysis, 32(1):227-245, 2012.
    • (2012) IMA Journal of Numerical Analysis , vol.32 , Issue.1 , pp. 227-245
    • Chen, C.1    He, B.2
  • 34
    • 84959366393 scopus 로고    scopus 로고
    • Matrix completion with column manipulation: Near-optimal sample-robustness-rank tradeoffs
    • Yudong Chen, Huan Xu, Constantine Caramanis, and Sujay Sanghavi. Matrix Completion with Column Manipulation: Near-Optimal Sample-Robustness-Rank Tradeoffs. IEEE Transactions on Information Theory, 62(1):503-526, 2016.
    • (2016) IEEE Transactions on Information Theory , vol.62 , Issue.1 , pp. 503-526
    • Chen, Y.1    Xu, H.2    Caramanis, C.3    Sanghavi, S.4
  • 38
    • 78049343675 scopus 로고    scopus 로고
    • Robust estimation of the vector autoregressive model by a least trimmed squares procedure
    • Christophe Croux and Kristel Joossens. Robust Estimation of the Vector Autoregressive Model by a Least Trimmed Squares Procedure. In Proceedings in Computational Statistics (COMPSTAT), 2008.
    • (2008) Proceedings in Computational Statistics (COMPSTAT)
    • Croux, C.1    Joossens, K.2
  • 42
    • 73149095169 scopus 로고    scopus 로고
    • Message passing algorithms for compressed sensing: I. Motivation and construction
    • David L. Donoho, Arian Maleki, and Andrea Montanari. Message Passing Algorithms for Compressed Sensing: I. Motivation and Construction. Proceedings of the National Academy of Sciences USA, 106(45):18914-18919, 2009.
    • (2009) Proceedings of the National Academy of Sciences USA , vol.106 , Issue.45 , pp. 18914-18919
    • Donoho, D.L.1    Maleki, A.2    Montanari, A.3
  • 45
    • 84887350278 scopus 로고    scopus 로고
    • Hankel matrix rank minimization with applications in system identification and realization
    • Maryam Fazel, Ting Kei Pong, Defeng Sun, and Paul Tseng. Hankel matrix rank minimization with applications in system identification and realization. SIAM Journal on Matrix Analysis and Applications, 34(3):946-977, 2013.
    • (2013) SIAM Journal on Matrix Analysis and Applications , vol.34 , Issue.3 , pp. 946-977
    • Fazel, M.1    Pong, T.K.2    Sun, D.3    Tseng, P.4
  • 46
    • 0019574599 scopus 로고
    • Random sample consensus: A paradigm for model fitting with applications to image analysis and automated cartography
    • Martin A. Fischler and Robert C. Bolles. Random Sample Consensus: A Paradigm for Model Fitting with Applications to Image Analysis and Automated Cartography. Communications of the ACM, 24(6):381-395, 1981.
    • (1981) Communications of the ACM , vol.24 , Issue.6 , pp. 381-395
    • Fischler, M.A.1    Bolles, R.C.2
  • 48
    • 84856034474 scopus 로고    scopus 로고
    • Hard thresholding pursuit: An algorithm for compressive sensing
    • Simon Foucart. Hard Thresholding Pursuit: an Algorithm for Compressive Sensing. SIAM Journal on Numerical Analysis, 49(6):2543-2563, 2011.
    • (2011) SIAM Journal on Numerical Analysis , vol.49 , Issue.6 , pp. 2543-2563
    • Foucart, S.1
  • 50
    • 0000474342 scopus 로고
    • Evidence for 2-chain helix in crystalline structure of sodium deoxyribonucleate
    • Rosalind Franklin and Raymond G. Gosling. Evidence for 2-Chain Helix in Crystalline Structure of Sodium Deoxyribonucleate. Nature, 172:156-157, 1953a.
    • (1953) Nature , vol.172 , pp. 156-157
    • Franklin, R.1    Gosling, R.G.2
  • 51
    • 0000812966 scopus 로고
    • Molecular configuration in sodium thymonucleate
    • Rosalind Franklin and Raymond G. Gosling. Molecular Configuration in Sodium Thymonucleate. Nature, 171:740-741, 1953b.
    • (1953) Nature , vol.171 , pp. 740-741
    • Franklin, R.1    Gosling, R.G.2
  • 55
    • 0015327061 scopus 로고
    • A practical algorithm for the determination of phase from image and diffraction plane pictures
    • R. W. Gerchberg and W. Owen Saxton. A Practical Algorithm for the Determination of Phase from Image and Diffraction Plane Pictures. Optik, 35 (2):237-246, 1972.
    • (1972) Optik , vol.35 , Issue.2 , pp. 237-246
    • Gerchberg, R.W.1    Owen Saxton, W.2
  • 57
    • 79952483985 scopus 로고    scopus 로고
    • Convergence of fixed-point continuation algorithms for matrix rank minimization
    • Donald Goldfarb and Shiqian Ma. Convergence of Fixed-Point Continuation Algorithms for Matrix Rank Minimization. Foundations of Computational Mathematics, 11(2):183-210, 2011.
    • (2011) Foundations of Computational Mathematics , vol.11 , Issue.2 , pp. 183-210
    • Goldfarb, D.1    Ma, S.2
  • 58
    • 0004236492 scopus 로고    scopus 로고
    • Johns Hopkins Studies in Mathematical Sciences. The John Hopkins University Press, 3rd edition
    • Gene H. Golub and Charles F. Van Loan. Matrix Computations. Johns Hopkins Studies in Mathematical Sciences. The John Hopkins University Press, 3rd edition, 1996.
    • (1996) Matrix Computations
    • Golub, G.H.1    Van Loan, C.F.2
  • 59
    • 84959441165 scopus 로고    scopus 로고
    • Sparse and spurious: Dictionary learning with noise and outliers
    • Rémi Gribonval, Rodolphe Jenatton, and Francis Bach. Sparse and Spurious: Dictionary Learning With Noise and Outliers. IEEE Transaction on Information Theory, 61(11):6298-6319, 2015.
    • (2015) IEEE Transaction on Information Theory , vol.61 , Issue.11 , pp. 6298-6319
    • Gribonval, R.1    Jenatton, R.2    Bach, F.3
  • 64
    • 85018503011 scopus 로고    scopus 로고
    • The restricted isometry property of subsampled fourier matrices
    • Bo'az Klartag and Emanuel Milman, editors Springer, Cham
    • Ishay Haviv and Oded Regev. The Restricted Isometry Property of Subsampled Fourier Matrices. In Bo'az Klartag and Emanuel Milman, editors, Geometric Aspects of Functional Analysis, Volume 2169 of Lecture Notes in Mathematics, pages 163-179. Springer, Cham, 2017.
    • (2017) Geometric Aspects of Functional Analysis, Volume 2169 of Lecture Notes in Mathematics , pp. 163-179
    • Haviv, I.1    Regev, O.2
  • 65
    • 84947791529 scopus 로고    scopus 로고
    • Wiley Series in Probability and Statistics. John Wiley & Sons, 2nd edition
    • Peter J. Huber and Elvezio M. Ronchetti. Robust Statistics. Wiley Series in Probability and Statistics. John Wiley & Sons, 2nd edition, 2009.
    • (2009) Robust Statistics
    • Huber, P.J.1    Ronchetti, E.M.2
  • 75
    • 0008142316 scopus 로고
    • The diameters of octahedra
    • Boris Sergeevich Kashin. The diameters of octahedra. Uspekhi Matematicheskikh Nauk, 30(4(184)):251-252, 1975.
    • (1975) Uspekhi Matematicheskikh Nauk , vol.30 , Issue.4-184 , pp. 251-252
    • Kashin, B.S.1
  • 78
    • 85008044987 scopus 로고    scopus 로고
    • Matrix factorization techniques for recommender systems
    • Yehuda Koren, Robert Bell, and Chris Volinsky. Matrix Factorization Techniques for. Recommender Systems. IEEE Computer, 42(8):30-37, 2009.
    • (2009) IEEE Computer , vol.42 , Issue.8 , pp. 30-37
    • Koren, Y.1    Bell, R.2    Volinsky, C.3
  • 80
    • 77955747588 scopus 로고    scopus 로고
    • ADMiRA: Atomic decomposition for minimum rank approximation
    • Kiryung Lee and Yoram Bresler. ADMiRA: Atomic Decomposition for Minimum Rank Approximation. IEEE Transactions on Information Theory, 56 (9):4402-4416, 2010.
    • (2010) IEEE Transactions on Information Theory , vol.56 , Issue.9 , pp. 4402-4416
    • Lee, K.1    Bresler, Y.2
  • 83
    • 43349087654 scopus 로고    scopus 로고
    • A-DNA and B-DNA: Comparing their historical X-ray fiber diffraction images
    • Amand A. Lucas. A-DNA and B-DNA: Comparing Their Historical X-ray Fiber Diffraction Images. Journal of Chemical Education, 85(5):737-743, 2008.
    • (2008) Journal of Chemical Education , vol.85 , Issue.5 , pp. 737-743
    • Lucas, A.A.1
  • 84
    • 0026678659 scopus 로고
    • On the convergence of the coordinate descent method for convex differentiable minimization
    • Zhi-Quan Luo and Paul Tseng. On the Convergence of the Coordinate Descent Method for Convex Differentiable Minimization. Journal of Optimization Theory and Applications, 72(1):7-35, 1992.
    • (1992) Journal of Optimization Theory and Applications , vol.72 , Issue.1 , pp. 7-35
    • Luo, Z.-Q.1    Tseng, P.2
  • 85
    • 21344480786 scopus 로고
    • Error bounds and convergence analysis of feasible descent methods: A general approach
    • Zhi-Quan Luo and Paul Tseng. Error bounds and convergence analysis of feasible descent methods: A general approach. Annals of Operations Research, 46(1):157-178, 1993.
    • (1993) Annals of Operations Research , vol.46 , Issue.1 , pp. 157-178
    • Luo, Z.-Q.1    Tseng, P.2
  • 89
    • 0029291966 scopus 로고
    • Sparse approximate solutions to linear systems
    • Balas Kausik Natarajan. Sparse approximate solutions to linear systems. SIAM Journal on Computing, 24(2):227-234, 1995.
    • (1995) SIAM Journal on Computing , vol.24 , Issue.2 , pp. 227-234
    • Natarajan, B.K.1
  • 90
    • 62749175137 scopus 로고    scopus 로고
    • CoSaMP: Iterative signal recovery from incomplete and inaccurate samples
    • Deanna Needell and Joel A. Tropp. CoSaMP: Iterative Signal Recovery from Incomplete and Inaccurate Samples. Applied and Computational Harmonic Analysis, 26:301-321, 2008.
    • (2008) Applied and Computational Harmonic Analysis , vol.26 , pp. 301-321
    • Needell, D.1    Tropp, J.A.2
  • 91
    • 84871600478 scopus 로고    scopus 로고
    • A unified framework for high-dimensional analysis of M-estimators with decomposable regularizers
    • Sahand N. Negahban, Pradeep Ravikumar, Martin J. Wainwright, and Bin Yu. A Unified Framework for High-Dimensional Analysis of M-Estimators with Decomposable Regularizers. Statistical Science, 27(4):538-557, 2012.
    • (2012) Statistical Science , vol.27 , Issue.4 , pp. 538-557
    • Negahban, S.N.1    Ravikumar, P.2    Wainwright, M.J.3    Yu, B.4
  • 94
    • 84865692149 scopus 로고    scopus 로고
    • Efficiency of coordinate descent methods on huge-scale optimization problems
    • Yurii Nesterov. Efficiency of Coordinate Descent Methods on Huge-Scale Optimization Problems. SIAM Journal of Optimization, 22(2):341-362, 2012.
    • (2012) SIAM Journal of Optimization , vol.22 , Issue.2 , pp. 341-362
    • Nesterov, Y.1
  • 95
    • 33646730150 scopus 로고    scopus 로고
    • Cubic regularization of newton method and its global performance
    • Yurii Nesterov and B.T. Polyak. Cubic regularization of Newton method and its global performance. Mathematical Programming, 108(1):177-205, 2006.
    • (2006) Mathematical Programming , vol.108 , Issue.1 , pp. 177-205
    • Nesterov, Y.1    Polyak, B.T.2
  • 97
    • 84896691347 scopus 로고    scopus 로고
    • Exact recoverability from dense corrupted observations via L1 minimization
    • Nam H. Nguyen and Trac D. Tran. Exact recoverability from dense corrupted observations via L1 minimization. IEEE Transactions on Information Theory, 59(4):2036-2058, 2013a.
    • (2013) IEEE Transactions on Information Theory , vol.59 , Issue.4 , pp. 2036-2058
    • Nguyen, N.H.1    Tran, T.D.2
  • 98
    • 84896691627 scopus 로고    scopus 로고
    • Robust lasso with missing and grossly corrupted observations
    • Nam H. Nguyen and Trac D. Tran. Robust Lasso With Missing and Grossly Corrupted Observations. IEEE Transaction on Information Theory, 59(4): 2036-2058, 2013b.
    • (2013) IEEE Transaction on Information Theory , vol.59 , Issue.4 , pp. 2036-2058
    • Nguyen, N.H.1    Tran, T.D.2
  • 100
    • 77956925453 scopus 로고    scopus 로고
    • Restricted eigenvalue properties for correlated Gaussian designs
    • Garvesh Raskutti, Martin J. Wainwright, and Bin Yu. Restricted Eigenvalue Properties for Correlated Gaussian Designs. Journal of Machine Learning Research, 11:2241-2259, 2010.
    • (2010) Journal of Machine Learning Research , vol.11 , pp. 2241-2259
    • Raskutti, G.1    Wainwright, M.J.2    Yu, B.3
  • 101
    • 84856009825 scopus 로고    scopus 로고
    • A simpler approach to matrix completion
    • Benjamin 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
  • 102
    • 78549288866 scopus 로고    scopus 로고
    • Guaranteed minimum rank solutions to linear matrix equations via nuclear norm minimization
    • Benjamin Recht, Maryam Fazel, and Pablo A. Parrilo. Guaranteed Minimum Rank Solutions to 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.A.3
  • 106
    • 84877774282 scopus 로고    scopus 로고
    • On the non-asymptotic convergence of cyclic coordinate descent methods
    • Ankan Saha and Ambuj Tewari. On the Non-asymptotic Convergence of Cyclic Coordinate Descent Methods. SIAM Journal on Optimization, 23 (1):576-601, 2013.
    • (2013) SIAM Journal on Optimization , vol.23 , Issue.1 , pp. 576-601
    • Saha, A.1    Tewari, A.2
  • 108
    • 84875134236 scopus 로고    scopus 로고
    • Stochastic dual coordinate ascent methods for regularized loss minimization
    • Shai Shalev-Shwartz and Tong Zhang. Stochastic Dual Coordinate Ascent Methods for Regularized Loss Minimization. Journal of Machine Learning Research, 14:567-599, 2013.
    • (2013) Journal of Machine Learning Research , vol.14 , pp. 567-599
    • Shalev-Shwartz, S.1    Zhang, T.2
  • 109
    • 79960141467 scopus 로고    scopus 로고
    • Outlier detection using nonconvex penalized regression
    • Yiyuan She and Art B. Owen. Outlier Detection Using Nonconvex Penalized Regression. Journal of the American Statistical Association, 106(494):626-639, 2011.
    • (2011) Journal of the American Statistical Association , vol.106 , Issue.494 , pp. 626-639
    • She, Y.1    Owen, A.B.2
  • 112
    • 84896973108 scopus 로고
    • Robust time series analysis: A survey
    • Norbert Stockinger and Rudolf Dutter. Robust time series analysis: A survey. Kybernetika, 23(7):1-3, 1987.
    • (1987) Kybernetika , vol.23 , Issue.7 , pp. 1-3
    • Stockinger, N.1    Dutter, R.2
  • 116
    • 84864315555 scopus 로고    scopus 로고
    • User-friendly tail bounds for sums of random matrices
    • Joel A. Tropp. User-Friendly Tail Bounds for Sums of Random Matrices. Foundations of Computational Mathematics, 12(4):389-434, 2012.
    • (2012) Foundations of Computational Mathematics , vol.12 , Issue.4 , pp. 389-434
    • Tropp, J.A.1
  • 117
    • 64649083745 scopus 로고    scopus 로고
    • Signal recovery from random measurements via orthogonal matching pursuit
    • Dec.
    • Joel A. Tropp and Anna C. Gilbert. Signal Recovery From Random Measurements Via Orthogonal Matching Pursuit. IEEE Transactions on Information Theory, 53(12):4655-4666, Dec. 2007. ISSN 0018-9448.
    • (2007) IEEE Transactions on Information Theory , vol.53 , Issue.12 , pp. 4655-4666
    • Tropp, J.A.1    Gilbert, A.C.2
  • 123
    • 0002210265 scopus 로고
    • On the convergence properties of the EM algorithm
    • C.-F. Jeff Wu. On the Convergence Properties of the EM Algorithm. The Annals of Statistics, 11(1):95-103, 1983.
    • (1983) The Annals of Statistics , vol.11 , Issue.1 , pp. 95-103
    • Jeff Wu, C.-F.1
  • 128
    • 84940000500 scopus 로고    scopus 로고
    • Recent advances in trust region algorithms
    • Ya-Xiang Yuan. Recent advances in trust region algorithms. Mathematical Programming, 151(1):249-281, 2015.
    • (2015) Mathematical Programming , vol.151 , Issue.1 , pp. 249-281
    • Yuan, Y.-X.1
  • 129
    • 79959549699 scopus 로고    scopus 로고
    • Adaptive forward-backward greedy algorithm for learning sparse representations
    • Tong Zhang. Adaptive Forward-Backward Greedy Algorithm for Learning Sparse Representations. IEEE Transactions on Information Theory, 57: 4689-4708, 2011.
    • (2011) IEEE Transactions on Information Theory , vol.57 , pp. 4689-4708
    • Zhang, T.1


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