Robust semi-supervised least squares classification by implicit constraints. (March 2017) - Krijthe, Jesse H.; Loog, Marco
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 and in terms of the expected classification error. Abstract : Highlights: A novel convex formulation for robust semi-supervised learning using squared loss. A proof that this procedure never reduces performance in terms of the squared loss for the 1-dimensional case without intercept. An empirical evaluation of the properties of this classifier.