Transforming classifier scores into accurate multiclass probability estimates

Class membership probability estimates are important for many applications of data mining in which classification outputs are combined with other sources of information for decision-making, such as example-dependent misclassification costs, the outputs of other classifiers, or domain knowledge. Previous calibration methods apply only to two-class problems. Here, we show how to obtain accurate probability estimates for multiclass problems by combining calibrated binary probability estimates. We also propose a new method for obtaining calibrated two-class probability estimates that can be applied to any classifier that produces a ranking of examples. Using naive Bayes and support vector machine classifiers, we give experimental results from a variety of two-class and multiclass domains, including direct marketing, text categorization and digit recognition.