Recent advances in Multiple Kernel Learning (MKL) have positioned it as an attractive tool for classification and regression. The development of efficient gradient descent based optimization schemes have made it possible to tackle large scale problems. Simultaneously, MKL based algorithms have defined the state-of-the-art on challenging real world applications. Yet, despite its success, MKL is limited in that it focuses on learning a linear combination of given base kernels. <p> In this paper, we observe that existing MKL formulations can be extended to learn general kernel combinations while retaining all the efficiency of existing large scale optimization algorithms. To highlight the advantages of generalized kernel learning, we tackle feature selection problems on benchmark vision and UCI databases. It is demonstrated that the proposed formulation can lead to better results not only as compared to traditional MKL but also compared to boosting, $l_1$ logistic regression, LP-SVM and Sparse-SVM.
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