Variational Bayesian inference for CP tensor completion with side information
Not on the map. Why?
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.
Key facts. Cited by 1 paper 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
20 of 86 references.
References · 20
- 2016Tensor Decomposition for Signal Processing and Machine Learningcited by 224
- 2018Nonconvex Optimization Meets Low-Rank Matrix Factorization: An Overviewcited by 160
- 2014Matrix Completion and Low-Rank SVD via Fast Alternating Least Squarescited by 104
- 2018Gradient Descent with Random Initialization: Fast Global Convergence for Nonconvex Phase Retrievalcited by 71
- 2014Bayesian CP Factorization of Incomplete Tensors with Automatic Rank Determinationcited by 65
- 2017Implicit Regularization in Nonconvex Statistical Estimation: Gradient Descent Converges Linearly for Phase Retrieval, Matrix Completion, and Blind Deconvolutioncited by 63
- 2016Efficient tensor completion for color image and video recovery: Low-rank tensor traincited by 61
- 2020Sparse Cholesky factorization by Kullback-Leibler minimizationcited by 41
- 2015Smooth PARAFAC Decomposition for Tensor Completioncited by 34
- 2013Provable Inductive Matrix Completioncited by 32
- 2014Bayesian Robust Tensor Factorization for Incomplete Multiway Datacited by 22
- 2015Fast Robust PCA on Graphscited by 13
8 more
- 2017Fast Low-Rank Bayesian Matrix Completion with Hierarchical Gaussian Prior Modelscited by 11
- 2013Rank regularization and Bayesian inference for tensor completion and extrapolationcited by 8
- 2015Bayesian Sparse Tucker Models for Dimension Reduction and Tensor Completioncited by 8
- 2021Tensor train completion: local recovery guarantees via Riemannian optimizationcited by 6
- 2018Coupled Graphs and Tensor Factorization for Recommender Systems and Community Detectioncited by 5
- 2021MTC: Multiresolution Tensor Completion from Partial and Coarse Observationscited by 4
- 2020Alternating minimization algorithms for graph regularized tensor completioncited by 3
- 2019Tuning Free Rank-Sparse Bayesian Matrix and Tensor Completion with Global-Local Priorscited by 1
Built on by
Citing papers per year: 2025: 1.
1 paper.