Learning Kernels for Structured Prediction using Polynomial Kernel Transformations

TL;DR

This paper introduces a novel method for learning structured kernels using polynomial transformations based on Schoenberg and Gegenbaur transforms, enhancing kernel learning for structured regression tasks.

Contribution

It proposes a new kernel learning approach using polynomial expansions and HSIC, with an efficient algorithm and state-of-the-art results on real datasets.

Findings

Achieved state-of-the-art performance on multiple datasets

Demonstrated effectiveness of polynomial kernel transformations

Provided an efficient matrix decomposition algorithm

Abstract

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.