  Production-grade recommender systems rely heavily on a large-scale corpus
used by online media services, including Netflix, Pinterest, and Amazon. These
systems enrich recommendations by learning users' and items' embeddings
projected in a low-dimensional space with two-stage models (two deep neural
networks), which facilitate their embedding constructs to predict users'
feedback associated with items. Despite its popularity for recommendations, its
theoretical behaviors remain comprehensively unexplored. We study the
asymptotic behaviors of the two-stage recommender that entail a strong
convergence to the optimal recommender system. We establish certain theoretical
properties and statistical assurance of the two-stage recommender. In addition
to asymptotic behaviors, we demonstrate that the two-stage recommender system
attains faster convergence by relying on the intrinsic dimensions of the input
features. Finally, we show numerically that the two-stage recommender enables
encapsulating the impacts of items' and users' attributes on ratings, resulting
in better performance compared to existing methods conducted using synthetic
and real-world data experiments.
