In many applications there is a need to monitor how a population is distributed across different classes, and to track the changes in this distribution that derive from varying circumstances, an example such application is monitoring the percentage (or "prevalence") of unemployed people in a given region, or in a given age range, or at different time periods. When the membership of an individual in a class cannot be established deterministically, this monitoring activity requires classification. However, in the above applications the final goal is not determining which class each individual belongs to, but simply estimating the prevalence of each class in the unlabeled data. This task is called quantification. In a supervised learning framework we may estimate the distribution across the classes in a test set from a training set of labeled individuals. However, this may be sub optimal, since the distribution in the test set may be substantially different from that in the training set (a phenomenon called distribution drift). So far, quantification has mostly been addressed by learning a classifier optimized for individual classification and later adjusting the distribution it computes to compensate for its tendency to either under-or over-estimate the prevalence of the class. In this paper we propose instead to use a type of decision trees (quantification trees) optimized not for individual classification, but directly for quantification. Our experiments show that quantification trees are more accurate than existing state-of-the-art quantification methods, while retaining at the same time the simplicity and understandability of the decision tree framework.
['Letizia Milli', 'Anna Monreale', 'Giulio Rossetti', 'Fosca Giannotti', 'Dino Pedreschi', 'Fabrizio Sebastiani']
Quantification Trees