Ranking from Incomplete Data

The most common classification setting is to predict labels from real-valued vectors, e.g. logistic regression or SupportVector Machines (SVM) are designed for this purpose. Our task differs from this: (1) The variables in our settings are defined over categorical domains with very many levels and there is no a priori knowledge about the space the variable instances lie in. (2) The observed data is highly sparse, nontrivial to interpret and it makes statements rather about pairs of instances than about a single instance. (3) The prediction problem is to rank the instances of one variable given an instance vector (the ‘context’) of the other variables. As the ranking should depend on the given instance vector, it is not a global ranking but a context dependent one. In this chapter, we discuss these three issues and develop a theory for context-aware ranking.