# Bayesian Robust Tensor Factorization for Incomplete Multiway Data

arXiv: https://arxiv.org/abs/1410.2386 · HTML: https://mlsanity.com/paper/1410.2386/

## Key facts

- Cited by 22 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 9 Oct 2014.

## Built on by (most cited first, 22 of 22)

- [Guaranteed Tensor Recovery Fused Low-rankness and Smoothness](https://mlsanity.com/paper/2302.02155/) (2023)
- [DeepTensor: Low-Rank Tensor Decomposition with Deep Network Priors](https://mlsanity.com/paper/2204.03145/) (2022)
- [Nonconvex Robust High-Order Tensor Completion Using Randomized Low-Rank Approximation](https://mlsanity.com/paper/2305.11495/) (2023)
- [Robust Factorization of Real-world Tensor Streams with Patterns, Missing Values, and Outliers](https://mlsanity.com/paper/2102.08466/) (2021)
- [Efficient Tensor Robust PCA under Hybrid Model of Tucker and Tensor Train](https://mlsanity.com/paper/2112.10771/) (2021)
- [Block-Term Tensor Decomposition Model Selection and Computation: The Bayesian Way](https://mlsanity.com/paper/2101.02931/) (2021)
- [Bayesian Low-rank Matrix Completion with Dual-graph Embedding: Prior Analysis and Tuning-free Inference](https://mlsanity.com/paper/2203.10044/) (2022)
- [Low-Rank Tensor Completion via Novel Sparsity-Inducing Regularizers](https://mlsanity.com/paper/2310.06233/) (2023)
- [Interpretable Bayesian Tensor Network Kernel Machines with Automatic Rank and Feature Selection](https://mlsanity.com/paper/2507.11136/) (2025)
- [Bayesian Robust Tensor Ring Model for Incomplete Multiway Data](https://mlsanity.com/paper/2202.13321/) (2022)
- [Variational Bayesian inference for CP tensor completion with side information](https://mlsanity.com/paper/2206.12486/) (2022)
- [A Novel Tensor Factorization-Based Method with Robustness to Inaccurate Rank Estimation](https://mlsanity.com/paper/2305.11458/) (2023)
- [Low-rank Bayesian matrix completion via geodesic Hamiltonian Monte Carlo on Stiefel manifolds](https://mlsanity.com/paper/2410.20318/) (2024)
- [Bayesian Fully-Connected Tensor Network for Hyperspectral-Multispectral Image Fusion](https://mlsanity.com/paper/2510.18400/) (2025)
- [Robust Manifold Nonnegative Tucker Factorization for Tensor Data Representation](https://mlsanity.com/paper/2211.03934/) (2022)
- [Low-Multi-Rank High-Order Bayesian Robust Tensor Factorization](https://mlsanity.com/paper/2311.05888/) (2023)
- [Adaptive Anomaly Detection in Network Flows with Low-Rank Tensor Decompositions and Deep Unrolling](https://mlsanity.com/paper/2409.11529/) (2024)
- [A Robust and Non-Iterative Tensor Decomposition Method with Automatic Thresholding](https://mlsanity.com/paper/2505.06203/) (2025)
- [Accelerating Large-Scale Regularized High-Order Tensor Recovery](https://mlsanity.com/paper/2506.09594/) (2025)
- [Robust Principal Component Completion](https://mlsanity.com/paper/2603.25132/) (2026)
- [Robust Low-Tubal-Rank Tensor Completion under Cross-Concentrated Sampling](https://mlsanity.com/paper/2608.03928/) (2026)
- [Bayesian Tensor Autoencoder with Physics-informed Predictive Prior for Multi-dimensional Time Series Anomaly Detection](https://mlsanity.com/paper/2609.31157/) (2026)

## Abstract (arXiv)

We propose a generative model for robust tensor factorization in the presence of both missing data and outliers. The objective is to explicitly infer the underlying low-CP-rank tensor capturing the global information and a sparse tensor capturing the local information (also considered as outliers), thus providing the robust predictive distribution over missing entries. The low-CP-rank tensor is modeled by multilinear interactions between multiple latent factors on which the column sparsity is enforced by a hierarchical prior, while the sparse tensor is modeled by a hierarchical view of Student-t distribution that associates an individual hyperparameter with each element independently. For model learning, we develop an efficient closed-form variational inference under a fully Bayesian treatment, which can effectively prevent the overfitting problem and scales linearly with data size. In contrast to existing related works, our method can perform model selection automatically and implicitly without need of tuning parameters. More specifically, it can discover the groundtruth of CP rank and automatically adapt the sparsity inducing priors to various types of outliers. In addition, the tradeoff between the low-rank approximation and the sparse representation can be optimized in the sense of maximum model evidence. The extensive experiments and comparisons with many state-of-the-art algorithms on both synthetic and real-world datasets demonstrate the superiorities of our method from several perspectives.