Column-generation boosting methods for mixture of kernels

We devise a boosting approach to classification and regression based on column generation using a mixture of kernels. Traditional kernel methods construct models based on a single positive semi-definite kernel with the type of kernel predefined and kernel parameters chosen according to cross-validation performance. Our approach creates models that are mixtures of a library of kernel models, and our algorithm automatically determines kernels to be used in the final model. The 1-norm and 2-norm regularization methods are employed to restrict the ensemble of kernel models. The proposed method produces sparser solutions, and thus significantly reduces the testing time. By extending the column generation (CG) optimization which existed for linear programs with 1-norm regularization to quadratic programs with 2-norm regularization, we are able to solve many learning formulations by leveraging various algorithms for constructing single kernel models. By giving different priorities to columns to be generated, we are able to scale CG boosting to large datasets. Experimental results on benchmark data are included to demonstrate its effectiveness.