A Pairwise Label Ranking Method with Imprecise Scores and Partial Predictions Sebastien Destercke Universit´ e de Technologie de Compiegne U.M.R. C.N.R.S. 7253 Heudiasyc Centre de recherches de Royallieu F-60205 Compiegne Cedex France sebastien.destercke@hds.utc.fr Abstract. In this paper, we are interested in the label ranking problem. We are more specifically interested in the recent trend consisting in predicting partial but more accurate (i.e., making less incorrect statements) orders rather than complete ones. To do so, we propose a ranking method based on pairwise imprecise scores obtained from likelihood functions. We discuss how such imprecise scores can be aggregated to produce interval orders, which are specific types of partial or- ders. We then analyse the performances of the method as well as its sensitivity to missing data and parameter values. Keywords: Label ranking, imprecise probabilities, Pairwise voting. 1 Introduction In recent years, learning problems with structured outputs have received a growing interest. Such problems appear in a variety of applications fields requiring to deal with complex data: natural language treatment [6], biological data [32], image analysis. . . In this paper, we are concerned with the problem of label ranking, where one has to learn a mapping from instances to rankings (complete orders) defined over a finite number of labels. Different methods have been proposed to perform this task. Ranking by pairwise comparison (RPC) [25] transforms the problem of label ranking into binary classification problems, combining all results to obtain the final ranking. Constraint classification and log-linear models [23,15] intend to learn, for each label, a (linear) utility function from which the ranking is deduced. Other approaches propose to fit a probabilistic ranking model (Mallows, Placket-Luce [28]) using different approaches (instance-based, linear models, etc. [29,10]). Recently, some authors [13] have discussed the interest, in label ranking and more generally in preference learning problems, to predict partial orders rather than complete rankings. Such an approach can be seen as an extension of the reject option imple- mented in learning problems [3] or of the fact of making partial predictions [14]. Such cautious predictions can prevent harmful decisions based on incorrect predictions. In practice, current methods [13] consist in thresholding a pairwise comparison matrix containing probabilistic estimates. More recently, it was shown [12] that probabilities issued from Placket-Luce and Mallows models are particularly interesting in such a thresholding approach, as they are guaranteed to produce consistent orders (i.e., with- out cycles) that belong to the family of semi-orders. H. Blockeel et al. (Eds.): ECML PKDD 2013, Part II, LNAI 8189, pp. 112–127, 2013. c  Springer-Verlag Berlin Heidelberg 2013