# Variational Bayesian inference for CP tensor completion with side information

arXiv: https://arxiv.org/abs/2206.12486 · HTML: https://mlsanity.com/paper/2206.12486/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 20 of its 86 references that are in the map.
- First posted on arXiv 24 Jun 2022.

## Builds on (most cited first, 20 of 20)

- [Tensor Decomposition for Signal Processing and Machine Learning](https://mlsanity.com/paper/1607.01668/) (2016)
- [Nonconvex Optimization Meets Low-Rank Matrix Factorization: An Overview](https://mlsanity.com/paper/1809.09573/) (2018)
- [Matrix Completion and Low-Rank SVD via Fast Alternating Least Squares](https://mlsanity.com/paper/1410.2596/) (2014)
- [Gradient Descent with Random Initialization: Fast Global Convergence for Nonconvex Phase Retrieval](https://mlsanity.com/paper/1803.07726/) (2018)
- [Bayesian CP Factorization of Incomplete Tensors with Automatic Rank Determination](https://mlsanity.com/paper/1401.6497/) (2014)
- [Implicit Regularization in Nonconvex Statistical Estimation: Gradient Descent Converges Linearly for Phase Retrieval, Matrix Completion, and Blind Deconvolution](https://mlsanity.com/paper/1711.10467/) (2017)
- [Efficient tensor completion for color image and video recovery: Low-rank tensor train](https://mlsanity.com/paper/1606.01500/) (2016)
- [Sparse Cholesky factorization by Kullback-Leibler minimization](https://mlsanity.com/paper/2004.14455/) (2020)
- [Smooth PARAFAC Decomposition for Tensor Completion](https://mlsanity.com/paper/1505.06611/) (2015)
- [Provable Inductive Matrix Completion](https://mlsanity.com/paper/1306.0626/) (2013)
- [Bayesian Robust Tensor Factorization for Incomplete Multiway Data](https://mlsanity.com/paper/1410.2386/) (2014)
- [Fast Robust PCA on Graphs](https://mlsanity.com/paper/1507.08173/) (2015)
- [Fast Low-Rank Bayesian Matrix Completion with Hierarchical Gaussian Prior Models](https://mlsanity.com/paper/1708.02455/) (2017)
- [Rank regularization and Bayesian inference for tensor completion and extrapolation](https://mlsanity.com/paper/1301.7619/) (2013)
- [Bayesian Sparse Tucker Models for Dimension Reduction and Tensor Completion](https://mlsanity.com/paper/1505.02343/) (2015)
- [Tensor train completion: local recovery guarantees via Riemannian optimization](https://mlsanity.com/paper/2110.03975/) (2021)
- [Coupled Graphs and Tensor Factorization for Recommender Systems and Community Detection](https://mlsanity.com/paper/1809.08353/) (2018)
- [MTC: Multiresolution Tensor Completion from Partial and Coarse Observations](https://mlsanity.com/paper/2106.07135/) (2021)
- [Alternating minimization algorithms for graph regularized tensor completion](https://mlsanity.com/paper/2008.12876/) (2020)
- [Tuning Free Rank-Sparse Bayesian Matrix and Tensor Completion with Global-Local Priors](https://mlsanity.com/paper/1905.11496/) (2019)

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

- [Large-Scale Bayesian Tensor Reconstruction via Approximate Message Passing](https://mlsanity.com/paper/2505.16305/) (2025)

## Abstract (arXiv)

We propose a message passing algorithm, based on variational Bayesian inference, for low-rank tensor completion with automatic rank determination in the canonical polyadic format when additional side information (SI) is given. The SI comes in the form of low-dimensional subspaces the contain the fiber spans of the tensor (columns, rows, tubes, etc.). We validate the regularization properties induced by SI with extensive numerical experiments on synthetic and real-world data and present the results about tensor recovery and rank determination. The results show that the number of samples required for successful completion is significantly reduced in the presence of SI. We also discuss the origin of a bump in the phase transition curves that exists when the dimensionality of SI is comparable with that of the tensor.