Factorization Models

In the last chapters, it was shown that a context-aware ranking \succ{\succ}\phantom{} can be expressed by a function or equivalently by a tensor in case of finite categorical domains X i . Estimating the full parametrized tensor Y is infeasible because (1) for real-world problems, the number of parameters (i.e. ) would be too large – e.g. for the Netflix problem we would need billions of parameters – and (2) even more important, that the observations are typically very sparse which results in poor estimates without any generalization capabilities.