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6 x 9, illustrated
ISSN
0899-7667
E-ISSN
1530-888X
2014 Impact factor:
2.21

Neural Computation

August 2018, Vol. 30, No. 8, Pages 2245-2283
(doi: 10.1162/neco_a_01096)
© 2018 Massachusetts Institute of Technology
A Comparative Study of Pairwise Learning Methods Based on Kernel Ridge Regression
Article PDF (423.87 KB)
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 past 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 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 into assessing the advantages and limitations of existing pairwise learning methods.