No abstract

We describe a monotone classification algorithm called MOCA that attempts to minimize the mean absolute prediction error for classification problems with ordered class labels. We first find a monotone classifier with minimum L 1 loss on the training sample, and then use a simple interpolation scheme to predict the class labels for attribute vectors not present in the training data. We compare MOCA to the Ordinal Stochastic Dominance Learner (OSDL), on artificial as well as real data sets. We show that MOCA often outperforms OSDL with respect to mean absolute prediction error.

Abstract. We propose a new algorithm for learning isotonic classification trees. It relabels non-monotone leaf nodes by performing the isotonic regression on the collection of leaf nodes. In case two leaf nodes with a common parent have the same class after relabeling, the tree is pruned in the parent node. Since we consider problems with ordered class labels, all results are evaluated on the basis of L1 prediction error. We experimentally compare the performance of the new algorithm with standard classification trees.

In many applications of data mining it is known beforehand that the response variable should be increasing (or decreasing) in the attributes. We propose two algorithms to exploit such monotonicity constraints for active learning in ordinal classification in two different settings. The basis of our approach is the observation that if the class label of an object is given, then the monotonicity constraints may allow the labels of other objects to be inferred. For instance, from knowing that loan applicant a is rejected, it can be concluded that all applicants that score worse than a on all criteria should be rejected as well. We propose two heuristics to select good query points. These heuristics make a selection based on a point's potential to determine the labels of other points. The algorithms, each implemented with the proposed heuristics, are evaluated on artificial and real data sets to study their performance. We conclude that exploitation of monotonicity constraints can be very beneficial in active learning. IntroductionIn many applications of data mining we know beforehand that the response variable is monotone (either increasing or decreasing) in one or more of the attributes. Consider, for example, the problem of ranking documents as {not relevant, somewhat relevant, relevant} with respect to a particular query. Typical attributes are (normalized) counts of query terms in the abstract or title of the document. One would expect an increasing relationship between these counts and document relevance. As another example, consider the problem of ranking loan applicants: it would be strange if applicant a scored at least as well as b on all criteria but were ranked worse than b in terms of credit risk.Most work in this area has focused on enforcing monotonicity constraints on the models learned from data, see for example [9,5,3]. In this paper, we consider the possibilities of exploiting monotonicity constraints for active learning in ordinal classification. The basis of our approach is the observation that if the class

Il existe une longue tradition d’études des Monti di Pietà, qui est presqu’entièrement publiée en italien. Cet article propose une revue historiographique de ces recherches, en se basant sur quatre thèmes centraux les ayant orientées. Le premier de ces thèmes correspond aux relations entre les banques et les premiers Monti, et à la question de savoir s’ils étaient de véritables banques ou des institutions charitables. Le deuxième thème correspond au contexte de ces pratiques formé par les débats théologiques et les opinions juridiques de la fin du Moyen Âge et de la Renaissance. Le troisième thème est centré sur l’influence des prédicateurs franciscains, incluant comment leurs discours antisémites ont été contrebalancés par les préoccupations économiques locales, pour former un compromis pratique. Le quatrième thème correspond au rôle et à la fonction qu’ont joués les Monti dans le Royaume de Naples. En conclusion, cette revue examine les recherches sur les Monti publiées en anglais depuis les années 1930.