Convex and Nonconvex Formulations for Mixed Regression With Two Components: Minimax Optimal Rates

作者: Yudong Chen , Xinyang Yi , Constantine Caramanis

DOI: 10.1109/TIT.2017.2773474

关键词:

摘要: … in Section III-D, and hence are minimax optimal. An interesting feature we observe is … a nonconvex yet tractable extension of the above convex program, for which we establish minimax …

参考文章(33)
Kert Viele, Barbara Tong, Modeling with Mixtures of Linear Regressions Statistics and Computing. ,vol. 12, pp. 315- 330 ,(2002) , 10.1023/A:1020779827503
Yuhong Yang, Andrew Barron, None, Information-theoretic determination of minimax rates of convergence Annals of Statistics. ,vol. 27, pp. 1564- 1599 ,(1999) , 10.1214/AOS/1017939142
Huan Xu, Yu-Xiang Wang, Noisy Sparse Subspace Clustering international conference on machine learning. pp. 89- 97 ,(2013)
Lucien Birg�, Approximation dans les espaces m�triques et th�orie de l'estimation Zeitschrift f�r Wahrscheinlichkeitstheorie und Verwandte Gebiete. ,vol. 65, pp. 181- 237 ,(1983) , 10.1007/BF00532480
E. Elhamifar, R. Vidal, Sparse Subspace Clustering: Algorithm, Theory, and Applications IEEE Transactions on Pattern Analysis and Machine Intelligence. ,vol. 35, pp. 2765- 2781 ,(2013) , 10.1109/TPAMI.2013.57
Daniel Hsu, Sham M. Kakade, Learning mixtures of spherical gaussians Proceedings of the 4th conference on Innovations in Theoretical Computer Science - ITCS '13. pp. 11- 20 ,(2013) , 10.1145/2422436.2422439
Moses Charikar, Sudipto Guha, Éva Tardos, David B. Shmoys, A constant-factor approximation algorithm for the k-median problem (extended abstract) symposium on the theory of computing. pp. 1- 10 ,(1999) , 10.1145/301250.301257
Mark Rudelson, Roman Vershynin, Hanson-Wright inequality and sub-gaussian concentration Electronic Communications in Probability. ,vol. 18, pp. 1- 9 ,(2013) , 10.1214/ECP.V18-2865
A. P. Dempster, N. M. Laird, D. B. Rubin, Maximum Likelihood from Incomplete Data Via theEMAlgorithm Journal of the Royal Statistical Society: Series B (Methodological). ,vol. 39, pp. 1- 22 ,(1977) , 10.1111/J.2517-6161.1977.TB01600.X
C. F. Jeff Wu, ON THE CONVERGENCE PROPERTIES OF THE EM ALGORITHM Annals of Statistics. ,vol. 11, pp. 95- 103 ,(1983) , 10.1214/AOS/1176346060