Optimal Thresholding of Classifiers to Maximize F1 Measure

• Published in: Machine Learning and Knowledge Discovery in Databases Vol. 8725; pp. 225 - 239
• Main Authors: Lipton, Zachary C., Elkan, Charles, Naryanaswamy, Balakrishnan
• Format: Book Chapter Journal Article
• Language: English
• Published: Germany Springer Berlin / Heidelberg 2014; Springer Berlin Heidelberg
• Series: Lecture Notes in Computer Science
• Subjects: Artificial intelligence; binary classification; Data mining; evaluation methodology; F score; F1 measure; multilabel learning; Pattern recognition; supervised learning; text classification; supervised learning; F1 measure; F score; multilabel learning; text classification; binary classification; evaluation methodology
• ISBN: 9783662448502; 3662448505
• ISSN: 0302-9743; 1611-3349
• DOI: 10.1007/978-3-662-44851-9_15

This paper provides new insight into maximizing F1 measures in the context of binary classification and also in the context of multilabel classification. The harmonic mean of precision and recall, the F1 measure is widely used to evaluate the success of a binary classifier when one class is rare. Micro average, macro average, and per instance average F1 measures are used in multilabel classification. For any classifier that produces a real-valued output, we derive the relationship between the best achievable F1 value and the decision-making threshold that achieves this optimum. As a special case, if the classifier outputs are well-calibrated conditional probabilities, then the optimal threshold is half the optimal F1 value. As another special case, if the classifier is completely uninformative, then the optimal behavior is to classify all examples as positive. When the actual prevalence of positive examples is low, this behavior can be undesirable. As a case study, we discuss the results, which can be surprising, of maximizing F1 when predicting 26,853 labels for Medline documents.