Multi-instance (MI) learning is a branch of machine learning, where each object (bag) consists of multiple feature vectors (instances)—for example, an image consisting of multiple patches and their corresponding feature vectors. In MI classification, each bag in the training set has a class label, but the instances are unlabeled. The instances are most commonly regarded as a set of points in a multi-dimensional space. Alternatively, instances are viewed as realizations of random vectors with corresponding probability distribution, where the bag is the distribution, not the realizations. By introducing the probability distribution space to bag-level classification problems, dissimilarities between probability distributions (divergences) can be applied. The bag-to-bag Kullback–Leibler information is asymptotically the best classifier, but the typical sparseness of MI training sets is an obstacle. We introduce bag-to-class divergence to MI learning, emphasizing the hierarchical nature of the random vectors that makes bags from the same class different. We propose two properties for bag-to-class divergences, and an additional property for sparse training sets, and propose a dissimilarity measure that fulfils them. Its performance is demonstrated on synthetic and real data. The probability distribution space is valid for MI learning, both for the theoretical analysis and applications.

Dataset: Breast tissue images available at https://bioimage.ucsb.edu/research/bio-segmentation, extracted feature vectors available at https://figshare.com/articles/MIProblems_A_repository_of_multiple_instance_learning_datasets/6633983. BreakHis data available at https://web.inf.ufpr.br/vri/databases/breast-cancer-histopathological-database-breakhis/. Code available at https://github.com/kajsam/ProbabilisticBag2Class.

Dataset License: CC BY 4.0