Superset Learning Based on Generalized Loss Minimization

In standard supervised learning, each training instance is associated with an outcome from a corresponding output space (e.g., a class label in classification or a real number in regression). In the superset learning problem, the outcome is only characterized in terms of a superset—a subset of candidates that covers the true outcome but may also contain additional ones. Thus, superset learning can be seen as a specific type of weakly supervised learning, in which training examples are ambiguous. In this paper, we introduce a generic approach to superset learning, which is motivated by the idea of performing model identification and "data disambiguation" simultaneously. This idea is realized by means of a generalized risk minimization approach, using an extended loss function that compares precise predictions with set-valued observations. As an illustration, we instantiate our meta learning technique for the problem of label ranking, in which the output space consists of all permutations of a fixed set of items. The label ranking method thus obtained is compared to existing approaches tackling the same problem.