Abstract: Ranking random observations has become essential to many data analysis problems, ranging from recommendation systems, computational biology, to information retrieval for instance. The information acquisition processes often involve various and poorly controlled sources however, leading to datasets possibly exhibiting strong sampling bias. The ability to rank observations is high-dimension is the subject of much attention, as being fundamental to nonparametric hypothesis testing when the observations are drawn from multiple independent distributions, especially due to the lack of natural relation order in the underlying space. 
 
In this talk, we will discuss an approach for ranking random observations of complex structure, when drawn from two unknown distributions, relying on a generalization of two-sample linear rank statistics. We will show how this new class encompasses and naturally extends classic univariate rank test statistics, namely for testing statistical independence. We will relate those problems to the concept of Receiver Operating Characteristic (ROC) curve, and provide finite sample guarantees of the testing errors. Convincing experimental studies will illustrate the advantages of this approach compared to state-of-the art methods. 
This is a joint work with S. Clémençon (Télécom Paris).

https://indico.math.cnrs.fr/event/12957/