Multiple Instance Learning via Covariant Aggregation

We present a multiple instance learning (MIL) algorithm that learns ellipsoidal decision boundaries with arbitrary covariance. In contrast to the fixed-length feature vectors of traditional classification problems, MIL operates on unordered bags of instances. Commonly, each instance is a feature vector, and a bag is considered positive if any one of its instances is positive. In training data, bags are labeled, rather than the instances themselves. Existing MIL approaches either do not acknowledge covariances that exist in the feature space or do not provide simple descriptions of the decision volumes. Our method learns simple volumes via incremental aggregation of volume-describing instances from the positive bags. Overall, we show effective and robust handling on low-dimensional, covariant learning problems, as well as competitive performance on standard MIL data sets.