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In binary classification, Learning from Positive and Unlabeled data (LePU) issemi-supervised learning but with labeled elements from only one class. Most ofthe research on LePU relies on some form of independence between the selectionprocess of annotated examples and the features of the annotated class, known asthe Selected Completely At Random (SCAR) assumption. Yet the annotation processis an important part of the data collection, and in many cases it naturallydepends on certain features of the data (e.g., the intensity of an image andthe size of the object to be detected in the image). Without any constraints onthe model for the annotation process, classification results in the LePUproblem will be highly non-unique. So proper, flexible constraints are needed.In this work we incorporate more flexible and realistic models for theannotation process than SCAR, and more importantly, offer a solution for thechallenging LePU problem. On the theory side, we establish the identifiabilityof the properties of the annotation process and the classification function, inlight of the considered constraints on the data-generating process. We alsopropose an inference algorithm to learn the parameters of the model, withsuccessful experimental results on both simulated and real data. We alsopropose a novel real-world dataset forLePU, as a benchmark dataset for futurestudies.

Learning from Positive and Unlabeled Data by Identifying the Annotation Process