A simple proof for the equivalence of multiple kernel regressors and single kernel regressors with sum of kernels

It is widely recognized that the kernel-based learning scheme is one of powerful tools in the field of machine learning. Recently, learning with multiple kernels, instead of a single kernel, attracts much attention in this field. Although their efficacy was investigated in terms of practical sense, their theoretical grounds were not sufficiently discussed in the past studies. In our previous work, we theoretically analyzed the standard 2-norm-based multiple-kernel regressor, and proved that the solution of the multiple kernel regressor obtained by 2-norm-based criterion reduces to the solution of the single kernel regressor with the sum of the kernels. However, the proof was hard to understand intuitively. In this work, we give a simple proof for the theorem in which the roles of the 2-norm-based criteria are intuitively convincing.