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

arXiv: https://arxiv.org/abs/1803.01575 · HTML: https://mlsanity.com/paper/1803.01575/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 5 Mar 2018.

## Built on by (most cited first, 3 of 3)

- [Multilinear Kernel Regression and Imputation via Manifold Learning](https://mlsanity.com/paper/2402.03648/) (2024)
- [Optimizing Estimators of Squared Calibration Errors in Classification](https://mlsanity.com/paper/2410.07014/) (2024)
- [StreaMRAK a Streaming Multi-Resolution Adaptive Kernel Algorithm](https://mlsanity.com/paper/2108.10411/) (2021)

## Abstract (arXiv)

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.