In many machine learning applications, precisely labeled data is either burdensome or impossible to collect. Multiple Instance Learning (MIL), in which training data is provided in the form of labeled bags rather than labeled instances, is one approach for dealing with ambiguously labeled data. In this paper we argue that in many applications of MIL (e.g. image, audio, text, bioinformatics) a single bag actually consists of a large or infinite number of instances, such as all points on a low dimensional manifold. For practical reasons, these bags get subsampled before training. Instead, we introduce a MIL formulation which directly models the underlying structure of these bags. We propose and analyze the query bag model, in which instances are obtained by repeatedly querying an oracle in a way that can capture relationships between instances. We show that sampling more instances results in better classification performance, which motivates us to develop algorithmic strategies for sampling many instances while maintaining efficiency.
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