A1 Refereed original research article in a scientific journal
Generalized vec trick for fast learning of pairwise kernel models
Authors: Viljanen Markus, Airola Antti, Pahikkala Tapio
Publisher: SPRINGER
Publication year: 2022
Journal: Machine Learning
Journal name in source: MACHINE LEARNING
Journal acronym: MACH LEARN
Volume: 111
Issue: 2
First page : 543
Last page: 573
Number of pages: 31
ISSN: 0885-6125
eISSN: 1573-0565
DOI: https://doi.org/10.1007/s10994-021-06127-y
Web address : https://link.springer.com/article/10.1007/s10994-021-06127-y
Self-archived copy’s web address: https://research.utu.fi/converis/portal/detail/Publication/69083033
Preprint address: https://arxiv.org/abs/2009.01054
Pairwise learning corresponds to the supervised learning setting where the goal is to make predictions for pairs of objects. Prominent applications include predicting drug-target or protein-protein interactions, or customer-product preferences. In this work, we present a comprehensive review of pairwise kernels, that have been proposed for incorporating prior knowledge about the relationship between the objects. Specifically, we consider the standard, symmetric and anti-symmetric Kronecker product kernels, metric-learning, Cartesian, ranking, as well as linear, polynomial and Gaussian kernels. Recently, a O(nm + nq) time generalized vec trick algorithm, where n, m, and q denote the number of pairs, drugs and targets, was introduced for training kernel methods with the Kronecker product kernel. This was a significant improvement over previous O(n(2)) training methods, since in most real-world applications m, q << n. In this work we show how all the reviewed kernels can be expressed as sums of Kronecker products, allowing the use of generalized vec trick for speeding up their computation. In the experiments, we demonstrate how the introduced approach allows scaling pairwise kernels to much larger data sets than previously feasible, and provide an extensive comparison of the kernels on a number of biological interaction prediction tasks.
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