  In semi-supervised learning, information from unlabeled examples is used to
improve the model learned from labeled examples. But in some learning problems,
partial label information can be inferred from otherwise unlabeled examples and
used to further improve the model. In particular, partial label information
exists when subsets of training examples are known to have the same label, even
though the label itself is missing. By encouraging a model to give the same
label to all such examples, we can potentially improve its performance. We call
this encouragement \emph{Nullspace Tuning} because the difference vector
between any pair of examples with the same label should lie in the nullspace of
a linear model. In this paper, we investigate the benefit of using partial
label information using a careful comparison framework over well-characterized
public datasets. We show that the additional information provided by partial
labels reduces test error over good semi-supervised methods usually by a factor
of 2, up to a factor of 5.5 in the best case. We also show that adding
Nullspace Tuning to the newer and state-of-the-art MixMatch method decreases
its test error by up to a factor of 1.8.

Machine Learning;Machine Learning