Obtaining Calibrated Probabilities from Boosting

Alexandru Niculescu-Mizil, Rich Caruana

Boosted decision trees typically yield good accuracy, precision, and ROC area. However, because the outputs from boosting are not well calibrated posterior probabilities, boosting yields poor squared error and cross-entropy. We empirically demonstrate why AdaBoost predicts distorted probabilities and examine three calibration methods for correcting this distortion: Platt Scaling, Isotonic Regression, and Logistic Correction. We also experiment with boosting using log-loss instead of the usual exponential loss. Experiments show that Logistic Correction and boosting with log-loss work well when boosting weak models such as decision stumps, but yield poor performance when boosting more complex models such as full decision trees. Platt Scaling and Isotonic Regression, however, significantly improve the probabilities predicted by both boosted stumps and boosted trees. After calibration, boosted full decision trees predict better probabilities than other learning methods such as SVMs, neural nets, bagged decision trees, and KNNs, even after these methods are calibrated.

Subjects: 12. Machine Learning and Discovery; Please choose a second document classification

Submitted: May 15, 2007

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