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Robust Semi-supervised Least Squares Classification by Implicit Constraints

Authors
  • Krijthe, Jesse H.
  • Loog, Marco
Type
Preprint
Publication Date
Dec 27, 2015
Submission Date
Dec 27, 2015
Identifiers
arXiv ID: 1512.08240
Source
arXiv
License
Yellow
External links

Abstract

We introduce the implicitly constrained least squares (ICLS) classifier, a novel semi-supervised version of the least squares classifier. This classifier minimizes the squared loss on the labeled data among the set of parameters implied by all possible labelings of the unlabeled data. Unlike other discriminative semi-supervised methods, this approach does not introduce explicit additional assumptions into the objective function, but leverages implicit assumptions already present in the choice of the supervised least squares classifier. This method can be formulated as a quadratic programming problem and its solution can be found using a simple gradient descent procedure. We prove that, in a limited 1-dimensional setting, this approach never leads to performance worse than the supervised classifier. Experimental results show that also in the general multidimensional case performance improvements can be expected, both in terms of the squared loss that is intrinsic to the classifier, as well as in terms of the expected classification error.

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