Efficient co-regularised least squares regression

  • Authors:
  • Ulf Brefeld;Thomas Gärtner;Tobias Scheffer;Stefan Wrobel

  • Affiliations:
  • Humboldt-Universität zu Berlin, Berlin, Germany;Fraunhofer AIS, Schloß Birlinghoven, Sankt Augustin, Germany;Humboldt-Universität zu Berlin, Berlin, Germany;University of Bonn, Germany

  • Venue:
  • ICML '06 Proceedings of the 23rd international conference on Machine learning
  • Year:
  • 2006

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Abstract

In many applications, unlabelled examples are inexpensive and easy to obtain. Semi-supervised approaches try to utilise such examples to reduce the predictive error. In this paper, we investigate a semi-supervised least squares regression algorithm based on the co-learning approach. Similar to other semi-supervised algorithms, our base algorithm has cubic runtime complexity in the number of unlabelled examples. To be able to handle larger sets of unlabelled examples, we devise a semi-parametric variant that scales linearly in the number of unlabelled examples. Experiments show a significant error reduction by co-regularisation and a large runtime improvement for the semi-parametric approximation. Last but not least, we propose a distributed procedure that can be applied without collecting all data at a single site.