Transforming classifier scores into accurate multiclass probability estimates

This work shows how to obtain accurate probability estimates for multiclass problems by combining calibrated binary probability estimates, and proposes a new method for obtaining calibrated two-class probability estimates that can be applied to any classifier that produces a ranking of examples.

Abstract

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.