# Scalable Bayesian Tensor Ring Factorization for Multiway Data Analysis

arXiv: https://arxiv.org/abs/2412.03321 · HTML: https://mlsanity.com/paper/2412.03321/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 11 of its 30 references that are in the map.
- First posted on arXiv 4 Dec 2024.

## Builds on (most cited first, 11 of 11)

- [Tensor Ring Decomposition](https://mlsanity.com/paper/1606.05535/) (2016)
- [Bayesian CP Factorization of Incomplete Tensors with Automatic Rank Determination](https://mlsanity.com/paper/1401.6497/) (2014)
- [Wide Compression: Tensor Ring Nets](https://mlsanity.com/paper/1802.09052/) (2018)
- [Efficient Low Rank Tensor Ring Completion](https://mlsanity.com/paper/1707.08184/) (2017)
- [Tensor Ring Decomposition with Rank Minimization on Latent Space: An Efficient Approach for Tensor Completion](https://mlsanity.com/paper/1809.02288/) (2018)
- [Bayesian Poisson Tucker Decomposition for Learning the Structure of International Relations](https://mlsanity.com/paper/1606.01855/) (2016)
- [Scalable Tucker Factorization for Sparse Tensors - Algorithms and Discoveries](https://mlsanity.com/paper/1710.02261/) (2017)
- [A Prior of a Googol Gaussians: a Tensor Ring Induced Prior for Generative Models](https://mlsanity.com/paper/1910.13148/) (2019)
- [Towards Flexible Sparsity-Aware Modeling: Automatic Tensor Rank Learning Using The Generalized Hyperbolic Prior](https://mlsanity.com/paper/2009.02472/) (2020)
- [Bayesian Sparse Tucker Models for Dimension Reduction and Tensor Completion](https://mlsanity.com/paper/1505.02343/) (2015)
- [Completion of High Order Tensor Data with Missing Entries via Tensor-train Decomposition](https://mlsanity.com/paper/1709.02641/) (2017)

## Built on by (most cited first, 2 of 2)

- [Large-Scale Bayesian Tensor Reconstruction via Approximate Message Passing](https://mlsanity.com/paper/2505.16305/) (2025)
- [Bayesian Tensor Decomposition with Diffusion Model Prior](https://mlsanity.com/paper/2606.03212/) (2026)

## Abstract (arXiv)

Tensor decompositions play a crucial role in numerous applications related to multi-way data analysis. By employing a Bayesian framework with sparsity-inducing priors, Bayesian Tensor Ring (BTR) factorization offers probabilistic estimates and an effective approach for automatically adapting the tensor ring rank during the learning process. However, previous BTR method employs an Automatic Relevance Determination (ARD) prior, which can lead to sub-optimal solutions. Besides, it solely focuses on continuous data, whereas many applications involve discrete data. More importantly, it relies on the Coordinate-Ascent Variational Inference (CAVI) algorithm, which is inadequate for handling large tensors with extensive observations. These limitations greatly limit its application scales and scopes, making it suitable only for small-scale problems, such as image/video completion. To address these issues, we propose a novel BTR model that incorporates a nonparametric Multiplicative Gamma Process (MGP) prior, known for its superior accuracy in identifying latent structures. To handle discrete data, we introduce the P'olya-Gamma augmentation for closed-form updates. Furthermore, we develop an efficient Gibbs sampler for consistent posterior simulation, which reduces the computational complexity of previous VI algorithm by two orders, and an online EM algorithm that is scalable to extremely large tensors. To showcase the advantages of our model, we conduct extensive experiments on both simulation data and real-world applications.