SpicyMKL: a fast algorithm for Multiple Kernel Learning with thousands of kernels

Abstract

We propose a new optimization algorithm for Multiple Kernel Learning (MKL) called SpicyMKL, which is applicable to general convex loss functions and general types of regularization. The proposed SpicyMKL iteratively solves smooth minimization problems. Thus, there is no need of solving SVM, LP, or QP internally. SpicyMKL can be viewed as a proximal minimization method and converges super-linearly. The cost of inner minimization is roughly proportional to the number of active kernels. Therefore, when we aim for a sparse kernel combination, our algorithm scales well against increasing number of kernels. Moreover, we give a general block-norm formulation of MKL that includes non-sparse regularizations, such as elastic-net and ℓ p -norm regularizations. Extending SpicyMKL, we propose an efficient optimization method for the general regularization framework. Experimental results show that our algorithm is faster than existing methods especially when the number of kernels is large (>1000).