A method for inferring label sampling mechanisms in semi-supervised learning

We consider the situation in semi-supervised learning, where the "label sampling" mechanism stochastically depends on the true response (as well as potentially on the features). We suggest a method of moments for estimating this stochastic dependence using the unlabeled data. This is potentially useful for two distinct purposes: A. As an input to a supervised learning procedure which can be used to "de-bias" its results using labeled data only and b. As a potentially interesting learning task in itself. We present several examples to illustrate the practical usefulness of our method.