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