# Rank regularization and Bayesian inference for tensor completion and extrapolation

arXiv: https://arxiv.org/abs/1301.7619 · HTML: https://mlsanity.com/paper/1301.7619/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 31 Jan 2013.

## Built on by (most cited first, 8 of 8)

- [Low Rank Optimization for Efficient Deep Learning: Making A Balance between Compact Architecture and Fast Training](https://mlsanity.com/paper/2303.13635/) (2023)
- [A high-order tensor completion algorithm based on Fully-Connected Tensor Network weighted optimization](https://mlsanity.com/paper/2204.01732/) (2022)
- [Streaming Generalized Canonical Polyadic Tensor Decompositions](https://mlsanity.com/paper/2110.14514/) (2021)
- [Variational Bayesian inference for CP tensor completion with side information](https://mlsanity.com/paper/2206.12486/) (2022)
- [Tensor Completion via Integer Optimization](https://mlsanity.com/paper/2402.05141/) (2024)
- [Adaptive Anomaly Detection in Network Flows with Low-Rank Tensor Decompositions and Deep Unrolling](https://mlsanity.com/paper/2409.11529/) (2024)
- [Variational Bayesian Inference for Tensor Robust Principal Component Analysis](https://mlsanity.com/paper/2412.18717/) (2024)
- [An Interdisciplinary and Cross-Task Review on Missing Data Imputation](https://mlsanity.com/paper/2511.01196/) (2025)

## Abstract (arXiv)

A novel regularizer of the PARAFAC decomposition factors capturing the tensor's rank is proposed in this paper, as the key enabler for completion of three-way data arrays with missing entries. Set in a Bayesian framework, the tensor completion method incorporates prior information to enhance its smoothing and prediction capabilities. This probabilistic approach can naturally accommodate general models for the data distribution, lending itself to various fitting criteria that yield optimum estimates in the maximum-a-posteriori sense. In particular, two algorithms are devised for Gaussian- and Poisson-distributed data, that minimize the rank-regularized least-squares error and Kullback-Leibler divergence, respectively. The proposed technique is able to recover the "ground-truth'' tensor rank when tested on synthetic data, and to complete brain imaging and yeast gene expression datasets with 50% and 15% of missing entries respectively, resulting in recovery errors at -10dB and -15dB.