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Sparse Semi-supervised Learning Using Conjugate Functions

Sun, S; Shawe-Taylor, J; (2010) Sparse Semi-supervised Learning Using Conjugate Functions. Journal of Machine Learning Research , 11 2423 - 2455. Green open access


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In this paper, we propose a general framework for sparse semi-supervised learning, which concerns using a small portion of unlabeled data and a few labeled data to represent target functions and thus has the merit of accelerating function evaluations when predicting the output of a new example. This framework makes use of Fenchel-Legendre conjugates to rewrite a convex insensitive loss involving a regularization with unlabeled data, and is applicable to a family of semi-supervised learning methods such as multi-view co-regularized least squares and single-view Laplacian support vector machines (SVMs). As an instantiation of this framework, we propose sparse multi-view SVMs which use a squared ε-insensitive loss. The resultant optimization is an inf-sup problem and the optimal solutions have arguably saddle-point properties. We present a globally optimal iterative algorithm to optimize the problem. We give the margin bound on the generalization error of the sparse multi-view SVMs, and derive the empirical Rademacher complexity for the induced function class. Experiments on artificial and real-world data show their effectiveness. We further give a sequential training approach to show their possibility and potential for uses in large-scale problems and provide encouraging experimental results indicating the efficacy of the margin bound and empirical Rademacher complexity on characterizing the roles of unlabeled data for semi-supervised learning

Type: Article
Title: Sparse Semi-supervised Learning Using Conjugate Functions
Open access status: An open access version is available from UCL Discovery
Publisher version: http://www.jmlr.org/papers/v11/sun10a.html
Language: English
Additional information: Copyright © 2010 Shiliang Sun and John Shawe-Taylor.
Keywords: semi-supervised learning, Fenchel-Legendre conjugate, representer theorem, multiview regularization, support vector machine, statistical learning theory
UCL classification: UCL > School of BEAMS > Faculty of Engineering Science > Computer Science
URI: http://discovery.ucl.ac.uk/id/eprint/399130
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