Learning Kernels for Structured Prediction using Polynomial Kernel Transformations
This work addresses the challenge of kernel learning for structured prediction, which is important for machine learning practitioners, but it appears incremental as it builds on existing kernel methods with specific transformations.
The paper tackles the problem of learning kernel functions for structured regression by proposing polynomial kernel transformations (Schoenberg and Gegenbaur transforms) to maximize dependency between input and output features using HSIC, and demonstrates state-of-the-art results on real-world datasets.
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.