Multiple instance learning via Gaussian processes

Multiple instance learning (MIL) is a binary classification problem with loosely supervised data where a class label is assigned only to a bag of instances indicating presence/absence of positive instances. In this paper we introduce a novel MIL algorithm using Gaussian processes (GP). The bag labeling protocol of the MIL can be effectively modeled by the sigmoid likelihood through the max function over GP latent variables. As the non-continuous max function makes exact GP inference and learning infeasible, we propose two approximations: the soft-max approximation and the introduction of witness indicator variables. Compared to the state-of-the-art MIL approaches, especially those based on the Support Vector Machine, our model enjoys two most crucial benefits: (i) the kernel parameters can be learned in a principled manner, thus avoiding grid search and being able to exploit a variety of kernel families with complex forms, and (ii) the efficient gradient search for kernel parameter learning effectively leads to feature selection to extract most relevant features while discarding noise. We demonstrate that our approaches attain superior or comparable performance to existing methods on several real-world MIL datasets including large-scale content-based image retrieval problems.