A Comparative Study of Pairwise Learning Methods based on Kernel Ridge Regression
This work provides theoretical insights for researchers in machine learning, but it is incremental as it reviews and unifies existing methods without introducing new algorithms.
The paper tackles the lack of theoretical analysis for kernel methods in pairwise learning by unifying existing kernel-based algorithms under Kronecker kernel ridge regression, showing that methods like independent task kernel ridge regression and linear matrix filtering minimize a squared loss and analyzing properties like universality and consistency.
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.