Title: Bridging Bag-Level and Instance-Level Uncertainty with Conformalizable MIL
Primary area: probabilistic methods (Bayesian methods, variational inference, sampling, UQ, etc.)
Keywords: Conformal Prediction, Multiple Instance Learning

Abstract: This paper introduces the concept of Conformalizable Multiple Instance Learning as well as a theoretical framework that establishes the connection between agnostic PAC learnability and the transferability of bag-level conformal prediction guarantees to individual instances. Our analysis defines rigorous conditions under which a calibrated conformal threshold provides reliable uncertainty quantification at both the bag and instance levels. We demonstrate that instance-level agnostic PAC learnability is both a necessary and sufficient condition to achieve valid instance-level coverage. Empirical evaluations on synthetic CIFAR-based tasks, Camelyon16 whole-slide images, and time series anomaly detection task validate our theoretical findings, confirming that agnostic PAC learnability underpins the conformalizability of existing MIL models. This work provides a robust theoretical and empirical foundation for integrating conformal prediction into MIL, offering valuable insights for enhancing uncertainty quantification in complex learning scenarios.