  While recommendation systems generally observe user behavior passively, there
has been an increased interest in directly querying users to learn their
specific preferences. In such settings, considering queries at different levels
of granularity to optimize user information acquisition is crucial to
efficiently providing a good user experience. In this work, we study the active
learning problem with multi-level user preferences within the collective matrix
factorization (CMF) framework. CMF jointly captures multi-level user
preferences with respect to items and relations between items (e.g., book
genre, cuisine type), generally resulting in improved predictions. Motivated by
finite-sample analysis of the CMF model, we propose a theoretically optimal
active learning strategy based on the Fisher information matrix and use this to
derive a realizable approximation algorithm for practical recommendations.
Experiments are conducted using both the Yelp dataset directly and an
illustrative synthetic dataset in the three settings of personalized active
learning, cold-start recommendations, and noisy data -- demonstrating strong
improvements over several widely used active learning methods.
