  While the success of semi-supervised learning (SSL) is still not fully
understood, Sch\"olkopf et al. (2012) have established a link to the principle
of independent causal mechanisms. They conclude that SSL should be impossible
when predicting a target variable from its causes, but possible when predicting
it from its effects. Since both these cases are somewhat restrictive, we extend
their work by considering classification using cause and effect features at the
same time, such as predicting disease from both risk factors and symptoms.
While standard SSL exploits information contained in the marginal distribution
of all inputs (to improve the estimate of the conditional distribution of the
target given inputs), we argue that in our more general setting we should use
information in the conditional distribution of effect features given causal
features. We explore how this insight generalises the previous understanding,
and how it relates to and can be exploited algorithmically for SSL.
