Computing regularization paths for learning multiple kernels

The problem of learning a sparse conic combination of kernel functions or kernel matrices for classification or regression can be achieved via the regularization by a block 1-norm [1]. In this paper, we present an al- gorithm that computes the entire regularization path for these problems. The path is obtained by using numerical continuation techniques, and involves a running time complexity that is a constant times the complex- ity of solving the problem for one value of the regularization parameter. Working in the setting of kernel linear regression and kernel logistic re- gression, we show empirically that the effect of the block 1-norm reg- ularization differs notably from the (non-block) 1-norm regularization commonly used for variable selection, and that the regularization path is of particular value in the block case.

Authors

• Francis Bach
• Romain Thibaux
• Michael Jordan

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