%K semi-supervised learning, Fenchel-Legendre conjugate, representer theorem, multiview regularization, support vector machine, statistical learning theory
%A S Sun
%A J Shawe-Taylor
%T Sparse Semi-supervised Learning Using Conjugate Functions
%J Journal of Machine Learning Research
%D 2010
%L discovery399130
%O Copyright © 2010 Shiliang Sun and John Shawe-Taylor.
%P 2423 - 2455
%V 11
%X 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