Multi-Instance Learning with Any Hypothesis Class

TL;DR

This paper provides a unified theoretical framework for Multiple-Instance Learning (MIL) applicable to any hypothesis class, demonstrating that MIL's sample complexity grows only poly-logarithmically with bag size and introducing a new PAC-learning algorithm based on standard supervised learning methods.

Contribution

The work offers a general theoretical analysis for MIL applicable to any hypothesis class and introduces a PAC-learning algorithm leveraging existing supervised learning algorithms.

Findings

Sample complexity depends poly-logarithmically on bag size.

Efficient PAC-learning for MIL is possible using standard supervised learning algorithms.

The proposed algorithm has polynomial complexity relative to bag size.

Abstract

In the supervised learning setting termed Multiple-Instance Learning (MIL), the examples are bags of instances, and the bag label is a function of the labels of its instances. Typically, this function is the Boolean OR. The learner observes a sample of bags and the bag labels, but not the instance labels that determine the bag labels. The learner is then required to emit a classification rule for bags based on the sample. MIL has numerous applications, and many heuristic algorithms have been used successfully on this problem, each adapted to specific settings or applications. In this work we provide a unified theoretical analysis for MIL, which holds for any underlying hypothesis class, regardless of a specific application or problem domain. We show that the sample complexity of MIL is only poly-logarithmically dependent on the size of the bag, for any underlying hypothesis class. In addition, we introduce a new PAC-learning algorithm for MIL, which uses a regular supervised learning algorithm as an oracle. We prove that efficient PAC-learning for MIL can be generated from any efficient non-MIL supervised learning algorithm that handles one-sided error. The computational complexity of the resulting algorithm is only polynomially dependent on the bag size.