Inverse M-Kernels for Linear Universal Approximators of Non-Negative Functions

Kernel methods are widely utilized in machine learning field to learn, from training data, a latent function in a reproducing kernel Hilbert space. It is well known that the approximator thus obtained usually achieves a linear representation, which brings various computational benefits, while maintaining great representation power (i.e., universal approximation). However, when non-negativity constraints are imposed on the function's outputs, the literature usually takes the kernel method-based approximators as offering linear representations at the expense of limited model flexibility or good representation power by allowing for their nonlinear forms. The main contribution of this paper is to derive a sufficient condition for a positive definite kernel so that it may construct flexible and linear approximators of non-negative functions. We call a kernel function that offers these attributes an inverse M-kernel; it is reminiscent of the inverse M-matrix.