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

References in zbMATH (referenced in 44 articles , 1 standard article )

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  1. Rachkovskij, D.A.: Binary vectors for fast distance and similarity estimation (2017)
  2. Schmidt, Mark; Le Roux, Nicolas; Bach, Francis: Minimizing finite sums with the stochastic average gradient (2017)
  3. Wang, Ximing; Fan, Neng; Pardalos, Panos M.: Stochastic subgradient descent method for large-scale robust chance-constrained support vector machines (2017)
  4. Gao, Wei; Wang, Lu; Jin, Rong; Zhu, Shenghuo; Zhou, Zhi-Hua: One-pass AUC optimization (2016)
  5. Lu, Jing; Hoi, Steven C.H.; Wang, Jialei; Zhao, Peilin; Liu, Zhi-Yong: Large scale online kernel learning (2016)
  6. Peña, Javier; Soheili, Negar: A deterministic rescaled perceptron algorithm (2016)
  7. Richtárik, Peter; Takáč, Martin: Distributed coordinate descent method for learning with big data (2016)
  8. Rosasco, Lorenzo; Villa, Silvia; Vũ, Bang C^ong: Stochastic forward-backward splitting for monotone inclusions (2016)
  9. Shalev-Shwartz, Shai; Zhang, Tong: Accelerated proximal stochastic dual coordinate ascent for regularized loss minimization (2016)
  10. Yang, Tianbao; Jin, Rong; Zhu, Shenghuo; Lin, Qihang: On data preconditioning for regularized loss minimization (2016)
  11. Do, Thanh-Nghi: Non-linear classification of massive datasets with a parallel algorithm of local support vector machines (2015) ioport
  12. Do, Thanh-Nghi; Poulet, François: Parallel multiclass logistic regression for classifying large scale image datasets (2015) ioport
  13. Mareček, Jakub; Richtárik, Peter; Takáč, Martin: Distributed block coordinate descent for minimizing partially separable functions (2015)
  14. Mokhtari, Aryan; Ribeiro, Alejandro: Global convergence of online limited memory BFGS (2015)
  15. Prasse, Paul; Sawade, Christoph; Landwehr, Niels; Scheffer, Tobias: Learning to identify concise regular expressions that describe email campaigns (2015)
  16. Xu, Yangyang; Yin, Wotao: Block stochastic gradient iteration for convex and nonconvex optimization (2015)
  17. Yang, Tianbao; Mahdavi, Mehrdad; Jin, Rong; Zhu, Shenghuo: An efficient primal dual prox method for non-smooth optimization (2015)
  18. Alama, Jesse; Heskes, Tom; Kühlwein, Daniel; Tsivtsivadze, Evgeni; Urban, Josef: Premise selection for mathematics by corpus analysis and kernel methods (2014)
  19. Couellan, Nicolas; Jan, Sophie: Incremental accelerated gradient methods for SVM classification: study of the constrained approach (2014)
  20. Ñanculef, Ricardo; Frandi, Emanuele; Sartori, Claudio; Allende, Héctor: A novel Frank-Wolfe algorithm. Analysis and applications to large-scale SVM training (2014)

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