Linear programs for automatic accuracy control in regression

Smola, AJ; Schölkopf, B; Rätsch, G

doi:10.1049/cp:19991171

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Linear programs for automatic accuracy control in regression

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https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=817991
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Smola, A., Schölkopf, B., & Rätsch, G. (1999). Linear programs for automatic accuracy control in regression. In Ninth International Conference on Artificial Neural Networks ICANN 99 (pp. 575-580). London, UK: Institute of Electrical Engineers.

Cite as: https://hdl.handle.net/11858/00-001M-0000-0013-E763-D

Abstract

We have recently proposed a new approach to control the number of basis functions and the accuracy in support vector machines. The latter is transferred to a linear programming setting, which inherently enforces sparseness of the solution. The algorithm computes a nonlinear estimate in terms of kernel functions and an /spl epsiv/>0 with the property that at most a fraction /spl nu/ of the training set has an error exceeding /spl epsiv/. The algorithm is robust to local perturbations of these points' target values. We give an explicit formulation of the optimization equations needed to solve the linear program and point out which modifications of the standard optimization setting are necessary to take advantage of the particular structure of the equations in the regression case.