Pegasos: Primal estimated sub-gradient solver for SVM

Pegasos: Primal estimated sub-gradient solver for SVM (2007)

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by Shai Shalev-Shwartz , Yoram Singer , Nathan Srebro

Venue:	IN ICML
Citations:	541 - 20 self

BibTeX

@INPROCEEDINGS{Shalev-Shwartz07pegasos:primal,
    author = {Shai Shalev-Shwartz and Yoram Singer and Nathan Srebro},
    title = {Pegasos: Primal estimated sub-gradient solver for SVM},
    booktitle = {IN ICML},
    year = {2007},
    pages = {807--814},
    publisher = {}
}

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Abstract

We describe and analyze a simple and effective iterative algorithm for solving the optimization problem cast by Support Vector Machines (SVM). Our method alternates between stochastic gradient descent steps and projection steps. We prove that the number of iterations required to obtain a solution of accuracy ǫ is Õ(1/ǫ). In contrast, previous analyses of stochastic gradient descent methods require Ω(1/ǫ2) 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 Õ(d/(λǫ)), 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 can seamlessly be adapted to employ non-linear kernels while working solely on the primal objective function. We demonstrate the efficiency and applicability of our approach by conducting experiments on large text classification problems, comparing our solver to existing state-of-the-art SVM solvers. For example, it takes less than 5 seconds for our solver to converge when solving a text classification problem from Reuters Corpus Volume 1 (RCV1) with 800,000 training examples.

Keyphrases

sub-gradient solver svm solver previous analysis stochastic gradient descent method large text classification problem total run-time optimization problem cast non-zero feature linear kernel large datasets regularization parameter primal objective function projection step effective iterative algorithm training example text classification problem training set support vector machine reuters corpus volume state-of-the-art svm solver non-linear kernel stochastic gradient descent step