Discriminative learning from partially annotated examples

A number of algorithms and its applications for automatic classifiers learning from examples is ever growing. Most of existing algorithms require a training set of completely annotated examples, which are often hard to obtain. In this thesis, we tackle the problem of learning from partially annotated examples, which means that each training input comes with a set of admissible labels only one of which is correct. We contributed to two different cases of this scenario. In the first case, we studied the problem of learning the ordinal classifiers from examples with interval annotation of labels. We designed a convex learning algorithm for this case and demonstrated its advantage on real data empirically. At the same time, we made several contributions to the supervised learning of the ordinal classifiers, namely, we proposed new parametrization of the ordinal classifier, we introduced more flexible piece wise version of the ordinal classifier, and we proposed a generic cutting plane solver with convergence guarantees. In the second case, we studied the problem of learning the structured output classifiers from examples with missing annotation of a subset of labels. We have defined the concept of a surrogate classification calibrated partial loss, the minimization of which guarantees that learning is statistical consistent under fairly general conditions on the data generating process. We proved the existence of a convex classification calibrated surrogate loss for learning from partially annotated examples. We showed which existing surrogate losses are classification calibrated and which are not. Our work thus provides a missing theoretical justification for so far heuristic methods which have been successfully used in practice.