# Variational Bayesian Inference for Tensor Robust Principal Component Analysis

arXiv: https://arxiv.org/abs/2412.18717 · HTML: https://mlsanity.com/paper/2412.18717/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 19 of its 59 references that are in the map.
- First posted on arXiv 25 Dec 2024.

## Builds on (most cited first, 19 of 19)

- [Variational Inference: A Review for Statisticians](https://mlsanity.com/paper/1601.00670/) (2016)
- [Tensor Robust Principal Component Analysis with A New Tensor Nuclear Norm](https://mlsanity.com/paper/1804.03728/) (2018)
- [Stable Low-rank Tensor Decomposition for Compression of Convolutional Neural Network](https://mlsanity.com/paper/2008.05441/) (2020)
- [Tensor Methods in Computer Vision and Deep Learning](https://mlsanity.com/paper/2107.03436/) (2021)
- [Guaranteed Tensor Recovery Fused Low-rankness and Smoothness](https://mlsanity.com/paper/2302.02155/) (2023)
- [Square Deal: Lower Bounds and Improved Relaxations for Tensor Recovery](https://mlsanity.com/paper/1307.5870/) (2013)
- [Robust Low-rank Tensor Recovery: Models and Algorithms](https://mlsanity.com/paper/1311.6182/) (2013)
- [Weighted Low-rank Tensor Recovery for Hyperspectral Image Restoration](https://mlsanity.com/paper/1709.00192/) (2017)
- [Multi-dimensional imaging data recovery via minimizing the partial sum of tubal nuclear norm](https://mlsanity.com/paper/1712.05870/) (2017)
- [On the Convergence of Coordinate Ascent Variational Inference](https://mlsanity.com/paper/2306.01122/) (2023)
- [Fast Low-Rank Bayesian Matrix Completion with Hierarchical Gaussian Prior Models](https://mlsanity.com/paper/1708.02455/) (2017)
- [Robust Tensor CUR Decompositions: Rapid Low-Tucker-Rank Tensor Recovery with Sparse Corruption](https://mlsanity.com/paper/2305.04080/) (2023)
- [Edge-promoting adaptive Bayesian experimental design for X-ray imaging](https://mlsanity.com/paper/2104.00301/) (2021)
- [Learning Sparse and Low-Rank Priors for Image Recovery via Iterative Reweighted Least Squares Minimization](https://mlsanity.com/paper/2304.10536/) (2023)
- [Rank regularization and Bayesian inference for tensor completion and extrapolation](https://mlsanity.com/paper/1301.7619/) (2013)
- [Alternating linear scheme in a Bayesian framework for low-rank tensor approximation](https://mlsanity.com/paper/2012.11228/) (2020)
- [Proximal MCMC for Bayesian Inference of Constrained and Regularized Estimation](https://mlsanity.com/paper/2205.07378/) (2022)
- [Sparse online variational Bayesian regression](https://mlsanity.com/paper/2102.12261/) (2021)
- [Leveraging joint sparsity in hierarchical Bayesian learning](https://mlsanity.com/paper/2303.16954/) (2023)

## Abstract (arXiv)

Tensor Robust Principal Component Analysis (TRPCA) holds a crucial position in machine learning and computer vision. It aims to recover underlying low-rank structures and to characterize the sparse structures of noise. Current approaches often encounter difficulties in accurately capturing the low-rank properties of tensors and balancing the trade-off between low-rank and sparse components, especially in a mixed-noise scenario. To address these challenges, we introduce a Bayesian framework for TRPCA, which integrates a low-rank tensor nuclear norm prior and a generalized sparsity-inducing prior. By embedding the priors within the Bayesian framework, our method can automatically determine the optimal tensor nuclear norm and achieve a balance between the nuclear norm and sparse components. Furthermore, our method can be efficiently extended to the weighted tensor nuclear norm model. Experiments conducted on synthetic and real-world datasets demonstrate the effectiveness and superiority of our method compared to state-of-the-art approaches.