swMATH ID: 8752
Software Authors: Shai Shalev-Shwartz, Yoram Singer, Nathan Srebro, Andrew Cotter
Description: Pegasos: primal estimated sub-gradient solver for SVM. We describe and analyze a simple and effective stochastic sub-gradient descent algorithm for solving the optimization problem cast by Support Vector Machines (SVM). We prove that the number of iterations required to obtain a solution of accuracy ϵ is O (1/ϵ) , where each iteration operates on a single training example. In contrast, previous analyses of stochastic gradient descent methods for SVMs require Ω(1/ϵ2) iterations. As in previously devised SVM solvers, the number of iterations also scales linearly with 1/λ, where λ is the regularization parameter of SVM. For a linear kernel, the total run-time of our method is O (d/(λϵ)) , where d is a bound on the number of non-zero features in each example. Since the run-time does not depend directly on the size of the training set, the resulting algorithm is especially suited for learning from large datasets. Our approach also extends to non-linear kernels while working solely on the primal objective function, though in this case the runtime does depend linearly on the training set size. Our algorithm is particularly well suited for large text classification problems, where we demonstrate an order-of-magnitude speedup over previous SVM learning methods
Homepage: http://link.springer.com/article/10.1007/s10107-010-0420-4
Related Software: LIBSVM; LIBLINEAR; UCI-ml; SVMlight; ImageNet; AdaGrad; SSVM; SGD-QN; RCV1; Forgetron; SIFT; AlexNet; Saga; L-BFGS; SeDuMi; Scikit; Matlab; RSVM; bmrm; LMNN
Referenced in: 103 Publications
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Referenced by 252 Authors

4 Richtárik, Peter
3 Jin, Rong
3 Takáč, Martin
3 Zhu, Shenghuo
2 Aggarwal, Charu C.
2 Bach, Francis R.
2 Couellan, Nicolas P.
2 Gao, Yang
2 Guo, Zheng-Chu
2 Iiduka, Hideaki
2 Lan, Guanghui
2 Landwehr, Niels
2 Patrascu, Andrei-Tudor
2 Phung, Dinh Q.
2 Piccialli, Veronica
2 Rosasco, Lorenzo A.
2 Sciandrone, Marco
2 Shalev-Shwartz, Shai
2 Shi, Lei
2 Villa, Silvia
2 Vũ, Bằng Công
2 Vucetic, Slobodan
2 Wang, Zhuang
2 Yang, Tianbao
2 Zhai, Tingting
1 Ahookhosh, Masoud
1 Alama, Jesse
1 Allende, Héctor
1 Asi, Hilal
1 Bai, Lan
1 Bai, Zuo
1 Bertsimas, Dimitris John
1 Bischl, Bernd
1 Blaschko, Matthew B.
1 Blondel, Mathieu
1 Bottou, Léon
1 Bshouty, Nader H.
1 Cao, Longbing
1 Carrizosa, Emilio
1 Chang, Yu-Ming
1 Chow, Yinlam
1 Cocianu, Catalina-Lucia
1 Cotter, Andrew
1 Csiba, Dominik
1 Cui, Jiangtao
1 Cuomo, Salvatore
1 Curtis, Frank E.
1 De Baets, Bernard
1 De Nicolao, Giuseppe
1 De Raedt, Luc
1 Demircioğlu, Aydin
1 Deng, Naiyang
1 Deng, Wan-Yu
1 Dieuleveut, Aymeric
1 Dinuzzo, Francesco
1 Djuric, Nemanja
1 Drozda, Paweł
1 Duchi, John C.
1 Durmus, Alain
1 Fan, Neng
1 Feng, Hui
1 Ferri, Francesc J.
1 Finley, Thomas
1 Frandi, Emanuele
1 Frasconi, Paolo
1 Gao, Kaifeng
1 Ghadimi, Saeed
1 Glasmachers, Tobias
1 Grimmer, Benjamin
1 Gu, Bin
1 Hao, Zhifeng
1 Hayes, David Neil
1 Hazan, Tamir
1 Heskes, Tom M.
1 Ho, Derek
1 Hoi, Steven C. H.
1 Holmes, Geoffrey
1 Horn, Daniel R.
1 Hsu, Chun-Nan
1 Hu, Bo
1 Huang, Guangbin
1 Huang, Han-Shen
1 Huang, Kaizhu
1 Huang, Lingxiao
1 Huerta, Ramón
1 Huo, Zenan
1 Irofti, Paul
1 Jain, Prateek
1 Jan, Sophie
1 Jawahar, C. V.
1 Jian, Ling
1 Jiang, Hui
1 Jiang, ZiDong
1 Jin, Yifei
1 Joachims, Thorsten
1 Jones, Andrew T.
1 Kimes, Patrick K.
1 Koriche, Frédéric
1 Kuang, Zhanghui
1 Kühlwein, Daniel
...and 152 more Authors
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Referenced in 47 Serials

14 Machine Learning
10 Journal of Machine Learning Research (JMLR)
7 Information Sciences
5 Neural Networks
5 SIAM Journal on Optimization
4 Mathematical Programming. Series A. Series B
4 Computational Optimization and Applications
4 International Journal of Computer Vision
3 Optimization Methods & Software
2 Optimization Letters
2 Statistical Analysis and Data Mining
1 Artificial Intelligence
1 The Annals of Statistics
1 Applied Mathematics and Optimization
1 Journal of Optimization Theory and Applications
1 Circuits, Systems, and Signal Processing
1 Bulletin of the Iranian Mathematical Society
1 Optimization
1 Computers & Operations Research
1 Journal of Automated Reasoning
1 International Journal of Approximate Reasoning
1 Annals of Operations Research
1 Neural Computation
1 Journal of Global Optimization
1 European Journal of Operational Research
1 Pattern Recognition
1 SIAM Review
1 Computational Statistics and Data Analysis
1 Cybernetics and Systems Analysis
1 Advances in Computational Mathematics
1 Mathematical Problems in Engineering
1 Soft Computing
1 Data Mining and Knowledge Discovery
1 International Journal of Applied Mathematics and Computer Science
1 Optimization and Engineering
1 4OR
1 Computational Management Science
1 Journal of Industrial and Management Optimization
1 Advances in Data Analysis and Classification. ADAC
1 Foundations and Trends in Machine Learning
1 Science China. Information Sciences
1 ISRN Applied Mathematics
1 EURO Journal on Computational Optimization
1 Computer Science Review
1 Springer Series in Statistics
1 International Journal of Systems Science. Principles and Applications of Systems and Integration
1 Japanese Journal of Statistics and Data Science

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