For semi-supervised techniques to be applied safely in practice we at least
want methods to outperform their supervised counterparts. We study this
question for classification using the well-known quadratic surrogate loss
function. Using a projection of the supervised estimate onto a set of
constraints imposed by the unlabeled data, we find we can safely improve over
the supervised solution in terms of this quadratic loss. Unlike other
approaches to semi-supervised learning, the procedure does not rely on
assumptions that are not intrinsic to the classifier at hand. It is
theoretically demonstrated that, measured on the labeled and unlabeled training
data, this semi-supervised procedure never gives a lower quadratic loss than
the supervised alternative. To our knowledge this is the first approach that
offers such strong, albeit conservative, guarantees for improvement over the
supervised solution. The characteristics of our approach are explicated using
benchmark datasets to further understand the similarities and differences
between the quadratic loss criterion used in the theoretical results and the
classification accuracy often considered in practice.

研究使用二次代理损失函数进行分类的半监督学习方法，通过对监督估计在未标记数据施加的一组约束的投影，我们发现我们可以安全地提高用于此二次损失的监督解决方案，这是第一种具有如此强大但保守保证的方法，而不依赖于分类器的原有假设。