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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.<\/jats:p>","DOI":"10.1162\/neco_a_01096","type":"journal-article","created":{"date-parts":[[2018,6,12]],"date-time":"2018-06-12T21:54:50Z","timestamp":1528840490000},"page":"2245-2283","source":"Crossref","is-referenced-by-count":25,"title":["A Comparative Study of Pairwise Learning Methods Based on Kernel Ridge Regression"],"prefix":"10.1162","volume":"30","author":[{"given":"Michiel","family":"Stock","sequence":"first","affiliation":[{"name":"KERMIT, Department of Data Analysis and Mathematical Modelling, Ghent University, 9000 Ghent, Belgium"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Tapio","family":"Pahikkala","sequence":"additional","affiliation":[{"name":"Department of Future Technologies, University of Turku, 20520 Turku, Finland"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Antti","family":"Airola","sequence":"additional","affiliation":[{"name":"Department of Future Technologies, University of Turku, 20520 Turku, Finland"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Bernard","family":"De Baets","sequence":"additional","affiliation":[{"name":"KERMIT, Department of Data Analysis and Mathematical Modelling, Ghent University, 9000 Ghent, Belgium"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Willem","family":"Waegeman","sequence":"additional","affiliation":[{"name":"KERMIT, Department of Data Analysis and Mathematical Modelling, Ghent University, 9000 Ghent, Belgium"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"281","reference":[{"key":"B1","first-page":"803","volume":"10","author":"Abernethy J.","year":"2008","journal-title":"Journal of Machine Learning Research"},{"key":"B2","author":"Adams R. 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