Probabilistic Score Estimation with Piecewise Logistic Regression

Abstract

Well-calibrated probabilities are necessary in many applications like probabilistic frameworks or cost-sensitive tasks. Based on previous success of asymmetric Laplace method in calibrating text classifiers' scores, we propose to use piecewise logistic regression, which is a simple extension of standard logistic regression, as an alternative method in the discriminative family. We show that both methods have the flexibility to be piecewise linear functions in log-odds, but they are based on quite different assumptions. We evaluated asymmetric Laplace method, piecewise logistic regression and standard logistic regression over standard text categorization collections (Reuters-21578 and TREC-AP) with three classifiers (SVM, Naive Bayes and Logistic Regression Classifier), and observed that piecewise logistic regression performs significantly better than the other two methods in the log-loss metric.