# A Simple and Scalable Tensor Completion Algorithm via Latent Invariant Constraint for Recommendation System

arXiv: https://arxiv.org/abs/2206.13355 · HTML: https://mlsanity.com/paper/2206.13355/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 7 of its 33 references that are in the map.
- First posted on arXiv 27 Jun 2022.

## Builds on (most cited first, 7 of 7)

- [A Survey on Session-based Recommender Systems](https://mlsanity.com/paper/1902.04864/) (2019)
- [Deep-IRT: Make Deep Learning Based Knowledge Tracing Explainable Using Item Response Theory](https://mlsanity.com/paper/1904.11738/) (2019)
- [Exact tensor completion with sum-of-squares](https://mlsanity.com/paper/1702.06237/) (2017)
- [Learning Distributed Representations from Reviews for Collaborative Filtering](https://mlsanity.com/paper/1806.06875/) (2018)
- [A Generalized Matrix Inverse with Applications to Robotic Systems](https://mlsanity.com/paper/1806.01776/) (2018)
- [A Scale-Consistent Approach for Recommender Systems](https://mlsanity.com/paper/1905.00055/) (2019)
- [A particle-based variational approach to Bayesian Non-negative Matrix Factorization](https://mlsanity.com/paper/1803.06321/) (2018)

## Abstract (arXiv)

In this paper we provide a latent-variable formulation and solution to the recommender system (RS) problem in terms of a fundamental property that any reasonable solution should be expected to satisfy. Specifically, we examine a novel tensor completion method to efficiently and accurately learn parameters of a model for the unobservable personal preferences that underly user ratings. By regularizing the tensor decomposition with a single latent invariant, we achieve three properties for a reliable recommender system: (1) uniqueness of the tensor completion result with minimal assumptions, (2) unit consistency that is independent of arbitrary preferences of users, and (3) a consensus ordering guarantee that provides consistent ranking between observed and unobserved rating scores. Our algorithm leads to a simple and elegant recommendation framework that has linear computational complexity and with no hyperparameter tuning. We provide empirical results demonstrating that the approach significantly outperforms current state-of-the-art methods.