Information-theoretic Classification Accuracy: A Criterion that Guides Data-driven Combination of Ambiguous Outcome Labels in Multi-class Classification

Outcome labeling ambiguity and subjectivity are ubiquitous in real-world datasets. While practitioners commonly combine ambiguous outcome labels in an ad hoc way to improve the accuracy of multi-class classification, there lacks a principled approach to guide label combination by any optimality criterion. To address this problem, we propose the information-theoretic classification accuracy (ITCA), a criterion of outcome "information" conditional on outcome prediction, to guide practitioners on how to combine ambiguous outcome labels. ITCA indicates a balance in the trade-off between prediction accuracy (how well do predicted labels agree with actual labels) and prediction resolution (how many labels are predictable). To find the optimal label combination indicated by ITCA, we develop two search strategies: greedy search and breadth-first search. Notably, ITCA and the two search strategies are adaptive to all machine-learning classification algorithms. Coupled with a classification algorithm and a search strategy, ITCA has two uses: to improve prediction accuracy and to identify ambiguous labels. We first verify that ITCA achieves high accuracy with both search strategies in finding the correct label combinations on synthetic and real data. Then we demonstrate the effectiveness of ITCA in diverse applications including medical prognosis, cancer survival prediction, user demographics prediction, and cell type classification.