  Object ranking is an important problem in the realm of preference learning.
On the basis of training data in the form of a set of rankings of objects,
which are typically represented as feature vectors, the goal is to learn a
ranking function that predicts a linear order of any new set of objects.
Current approaches commonly focus on ranking by scoring, i.e., on learning an
underlying latent utility function that seeks to capture the inherent utility
of each object. These approaches, however, are not able to take possible
effects of context-dependence into account, where context-dependence means that
the utility or usefulness of an object may also depend on what other objects
are available as alternatives. In this paper, we formalize the problem of
context-dependent ranking and present two general approaches based on two
natural representations of context-dependent ranking functions. Both approaches
are instantiated by means of appropriate neural network architectures, which
are evaluated on suitable benchmark task.
