Pegasos: Primal Estimated sub-gradient solver for SVM

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Pegasos: Primal Estimated sub-gradient solver for SVM

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by Shai Shalev-Shwartz , Yoram Singer , Nathan Srebro , Andrew Cotter

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542 - 20 self

BibTeX

@MISC{Shalev-Shwartz_pegasos:primal,
    author = {Shai Shalev-Shwartz and Yoram Singer and Nathan Srebro and Andrew Cotter},
    title = {Pegasos: Primal Estimated sub-gradient solver for SVM },
    year = {}
}

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Abstract

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 ɛ is Õ(1/ɛ), where each iteration operates on a single training example. In contrast, previous analyses of stochastic gradient descent methods for SVMs require Ω(1/ɛ2) 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/(λɛ)), 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.

Keyphrases

sub-gradient solver large text classification problem total run-time large datasets non-zero feature regularization parameter optimization problem cast linear kernel non-linear kernel svms require svm solver single training example training set support vector machine primal objective function previous analysis effective stochastic sub-gradient descent algorithm previous svm learning method order-of-magnitude speedup stochastic gradient descent method

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