Controlling false positives in multiple instance learning: The “c-rule” approach

This paper introduces a novel strategy for labeling bags in binary Multiple Instance Learning (MIL) under the standard MI assumption . The proposed approach addresses errors in instance labeling by classifying a bag as positive if it contains at least c positively labeled instances. This strategy seeks to balance the trade-off between controlling the false positive rate (mislabeling a negative bag as positive) and the false negative rate (mislabeling a positive bag as negative) while reducing labeling efforts. The study provides theoretical justifications for this approach and introduces algorithms for its implementation, including determining the minimum value of c required to keep error rates below predefined thresholds. Additionally, it proposes a methodology to estimate the number of genuinely positive and negative instances within bags. Simulations demonstrate the superior performance of the “ c -rule” compared to the standard rule (corresponding to c = 1 ) in scenarios with sparse positive bags and moderately low to high probability of misclassifying a negative instance. This trend is further validated through comparisons using two real-world datasets. Overall, this research advances the understanding of error management in MIL and provides practical tools for real-world applications. • Proposes a new method to handle type I/II errors in bag labeling with noise at the instance level. • Classifies a bag as positive in binary MIL if it contains at least c instances labeled as positive. • Offers an algorithm to find the minimum c ensuring type I/II error probabilities stay below set thresholds. • The method is theory-based, with results rigorously stated and proved. • Simulations and real-world data show the method outperforms the standard rule ( c = 1 ) in sparse positive bag scenarios.