  Normalized nonnegative models assign probability distributions to users and
random variables to items; see [Stark, 2015]. Rating an item is regarded as
sampling the random variable assigned to the item with respect to the
distribution assigned to the user who rates the item. Models of that kind are
highly expressive. For instance, using normalized nonnegative models we can
understand users' preferences as mixtures of interpretable user stereotypes,
and we can arrange properties of users and items in a hierarchical manner.
These features would not be useful if the predictive power of normalized
nonnegative models was poor. Thus, we analyze here the performance of
normalized nonnegative models for top-N recommendation and observe that their
performance matches the performance of methods like PureSVD which was
introduced in [Cremonesi et al., 2010]. We conclude that normalized nonnegative
models not only provide accurate recommendations but they also deliver (for
free) representations that are interpretable. We deepen the discussion of
normalized nonnegative models by providing further theoretical insights. In
particular, we introduce total variational distance as an operational
similarity measure, we discover scenarios where normalized nonnegative models
yield unique representations of users and items, we prove that the inference of
optimal normalized nonnegative models is NP-hard and finally, we discuss the
relationship between normalized nonnegative models and nonnegative matrix
factorization.
