An Admissible Shift-Consistent Method for Recommender Systems

TL;DR

This paper introduces a shift-consistency constraint for recommender systems that ensures mathematical robustness, fairness, and admissibility, extending from matrices to tensors to handle complex user-product relationships.

Contribution

It presents a novel shift-consistency constraint that guarantees admissibility, fairness, and robustness in matrix and tensor completion for recommender systems.

Findings

Guarantees admissibility and fairness in recommendations

Ensures robustness through unique missing-value imputation

Extends to tensor form for complex data structures

Abstract

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.