# An Admissible Shift-Consistent Method for Recommender Systems

arXiv: https://arxiv.org/abs/2307.08857 · HTML: https://mlsanity.com/paper/2307.08857/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 6 of its 32 references that are in the map.
- First posted on arXiv 17 Jul 2023.

## Builds on (most cited first, 6 of 6)

- [Guaranteed Matrix Completion via Non-convex Factorization](https://mlsanity.com/paper/1411.8003/) (2014)
- [Understanding Alternating Minimization for Matrix Completion](https://mlsanity.com/paper/1312.0925/) (2013)
- [A Max-Norm Constrained Minimization Approach to 1-Bit Matrix Completion](https://mlsanity.com/paper/1309.6013/) (2013)
- [Matrix Completion via Max-Norm Constrained Optimization](https://mlsanity.com/paper/1303.0341/) (2013)
- [Low-Rank Tensor Completion by Truncated Nuclear Norm Regularization](https://mlsanity.com/paper/1712.00704/) (2017)
- [Tensor Completion with Provable Consistency and Fairness Guarantees for Recommender Systems](https://mlsanity.com/paper/2204.01815/) (2022)

## Abstract (arXiv)

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.