# A generalizable framework for low-rank tensor completion with numerical priors

arXiv: https://arxiv.org/abs/2302.05881 · HTML: https://mlsanity.com/paper/2302.05881/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 13 of its 56 references that are in the map.
- First posted on arXiv 12 Feb 2023.

## Builds on (most cited first, 13 of 13)

- [Exact tensor completion using t-SVD](https://mlsanity.com/paper/1502.04689/) (2015)
- [Bayesian CP Factorization of Incomplete Tensors with Automatic Rank Determination](https://mlsanity.com/paper/1401.6497/) (2014)
- [Tensor Completion Algorithms in Big Data Analytics](https://mlsanity.com/paper/1711.10105/) (2017)
- [Efficient Low Rank Tensor Ring Completion](https://mlsanity.com/paper/1707.08184/) (2017)
- [Nonconvex Low-Rank Tensor Completion from Noisy Data](https://mlsanity.com/paper/1911.04436/) (2019)
- [Smooth PARAFAC Decomposition for Tensor Completion](https://mlsanity.com/paper/1505.06611/) (2015)
- [Generalized Canonical Polyadic Tensor Decomposition](https://mlsanity.com/paper/1808.07452/) (2018)
- [A Nonconvex Low-Rank Tensor Completion Model for Spatiotemporal Traffic Data Imputation](https://mlsanity.com/paper/2003.10271/) (2020)
- [A single gradient step finds adversarial examples on random two-layers neural networks](https://mlsanity.com/paper/2104.03863/) (2021)
- [Noisy Tensor Completion via Low-rank Tensor Ring](https://mlsanity.com/paper/2203.08857/) (2022)
- [Nonnegative Tensor Completion via Integer Optimization](https://mlsanity.com/paper/2111.04580/) (2021)
- [Tensor Completion with Provable Consistency and Fairness Guarantees for Recommender Systems](https://mlsanity.com/paper/2204.01815/) (2022)
- [Logistic Tensor Factorization for Multi-Relational Data](https://mlsanity.com/paper/1306.2084/) (2013)

## Built on by (most cited first, 1 of 1)

- [Efficient Tensor Completion Algorithms for Highly Oscillatory Operators](https://mlsanity.com/paper/2510.17734/) (2025)

## Abstract (arXiv)

Low-Rank Tensor Completion, a method which exploits the inherent structure of tensors, has been studied extensively as an effective approach to tensor completion. Whilst such methods attained great success, none have systematically considered exploiting the numerical priors of tensor elements. Ignoring numerical priors causes loss of important information regarding the data, and therefore prevents the algorithms from reaching optimal accuracy. Despite the existence of some individual works which consider ad hoc numerical priors for specific tasks, no generalizable frameworks for incorporating numerical priors have appeared. We present the Generalized CP Decomposition Tensor Completion (GCDTC) framework, the first generalizable framework for low-rank tensor completion that takes numerical priors of the data into account. We test GCDTC by further proposing the Smooth Poisson Tensor Completion (SPTC) algorithm, an instantiation of the GCDTC framework, whose performance exceeds current state-of-the-arts by considerable margins in the task of non-negative tensor completion, exemplifying GCDTC's effectiveness. Our code is open-source.