  Learning the kernel functions used in kernel methods has been a vastly
explored area in machine learning. It is now widely accepted that to obtain
'good' performance, learning a kernel function is the key challenge. In this
work we focus on learning kernel representations for structured regression. We
propose use of polynomials expansion of kernels, referred to as Schoenberg
transforms and Gegenbaur transforms, which arise from the seminal result of
Schoenberg (1938). These kernels can be thought of as polynomial combination of
input features in a high dimensional reproducing kernel Hilbert space (RKHS).
We learn kernels over input and output for structured data, such that,
dependency between kernel features is maximized. We use Hilbert-Schmidt
Independence Criterion (HSIC) to measure this. We also give an efficient,
matrix decomposition-based algorithm to learn these kernel transformations, and
demonstrate state-of-the-art results on several real-world datasets.
