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We have presented a new decomposition algorithm intended to efficiently solve large-scale regression problems using SVMs. This algorithm followed the same principles as those used by Joachims [5] in his classification algorithm. Compared to previously proposed decomposition algorithms for regression, we have proposed an original method to select the variables in the working set. We have shown how to solve analytically subproblems of size 2, as it is done in SMO [12]. An internal cache keeping part of the kernel matrix in memory enables the program to solve large problems without the need to keep quadratic resources in memory and without the need to recompute every kernel evaluation, which leads to an overall fast algorithm. We have also shown that there exists a convergence proof for our algorithm. Finally, an experimental comparison with another algorithm has shown significant time improvement for large-scale problems and training time generally scaling slightly less than quadratically with respect to the number of examples.

Journal of Machine Learning Research