Nonparametric active learning for cost-sensitive classification

For many real-world machine learning tasks, while unlabelled data are abundant, getting a pool of labelled data is very expensive and time-consuming. In this case, it is interesting to only label the points that could significantly affect the prediction decision. This is the main purpose of active learning (Cohn et al., 1994; Dasgupta, 2011) which is a machine learning approach that attemps to provide an optimal decision rule while using as few labelled data as possible. Contrary to standard models of machine learning (namely passive learning) where the labelled data are provided beforehand, in active learning, the learner only has access to a set of unlabelled points at the beginning, and has to progressively request (to a so-called oracle) at some cost the label of some points during the learning process. At the end, based on these selected labelled points, a prediction decision rule is provided. In this paper, we consider the classification task which consists in providing a prediction rule or classifier that maps each unlabelled point x from X, the instance space, to an element y Y = {1,...,M} the label space (where M 2 is an integer). Both in active and in passive learning, the performance of a prediction rule is measured in terms of its ability to predict the label of a new instance by keeping the error of classification as small as possible. However, while fruitful in many domains applications, measuring the performance of a classifier by only considering its ability to maintain the error of classification as small as possible is sometimes inappropriate because some type of classification errors (even small) could have significant negative effects on the underlying problem. For many real world domain applications, it is thus valuable to consider learning classification approaches that pay attention to each error of classification.