A Comparative Study of Pairwise Learning Methods based on Kernel Ridge Regression

TL;DR

This paper reviews and unifies kernel-based pairwise learning methods, analyzing their theoretical properties and demonstrating their relationships through Kronecker kernel ridge regression.

Contribution

It provides a comprehensive theoretical analysis and unification of various kernel-based pairwise learning algorithms, highlighting their implicit loss minimization and spectral properties.

Findings

All methods implicitly minimize squared loss

Analysis of universality and consistency

Spectral filtering properties elucidated

Abstract

Many machine learning problems can be formulated as predicting labels for a pair of objects. Problems of that kind are often referred to as pairwise learning, dyadic prediction or network inference problems. During the last decade kernel methods have played a dominant role in pairwise learning. They still obtain a state-of-the-art predictive performance, but a theoretical analysis of their behavior has been underexplored in the machine learning literature. In this work we review and unify existing kernel-based algorithms that are commonly used in different pairwise learning settings, ranging from matrix filtering to zero-shot learning. To this end, we focus on closed-form efficient instantiations of Kronecker kernel ridge regression. We show that independent task kernel ridge regression, two-step kernel ridge regression and a linear matrix filter arise naturally as a special case of Kronecker kernel ridge regression, implying that all these methods implicitly minimize a squared loss. In addition, we analyze universality, consistency and spectral filtering properties. Our theoretical results provide valuable insights in assessing the advantages and limitations of existing pairwise learning methods.