An Admissible Shift-Consistent Method for Recommender Systems
Tung Nguyen Jeffrey Uhlmann
In this paper, we propose a new constraint, called shift-consistency, for
solving matrix/tensor completion problems in the context of recommender
systems. Our method provably guarantees several key mathematical properties:
(1) satisfies a recently established admissibility criterion for recommender
systems; (2) satisfies a definition of fairness that eliminates a specific
class of potential opportunities for users to maliciously influence system
recommendations; and (3) offers robustness by exploiting provable uniqueness of
missing-value imputation. We provide a rigorous mathematical description of the
method, including its generalization from matrix to tensor form to permit
representation and exploitation of complex structural relationships among sets
of user and product attributes. We argue that our analysis suggests a
structured means for defining latent-space projections that can permit provable
performance properties to be established for machine learning methods.