# Bayesian Sparse Tucker Models for Dimension Reduction and Tensor Completion

arXiv: https://arxiv.org/abs/1505.02343 · HTML: https://mlsanity.com/paper/1505.02343/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 10 May 2015.

## Built on by (most cited first, 8 of 8)

- [Rethinking Bayesian Learning for Data Analysis: The Art of Prior and Inference in Sparsity-Aware Modeling](https://mlsanity.com/paper/2205.14283/) (2022)
- [Block-Term Tensor Decomposition Model Selection and Computation: The Bayesian Way](https://mlsanity.com/paper/2101.02931/) (2021)
- [To Fold or Not to Fold: Graph Regularized Tensor Train for Visual Data Completion](https://mlsanity.com/paper/2306.11123/) (2023)
- [Interpretable Bayesian Tensor Network Kernel Machines with Automatic Rank and Feature Selection](https://mlsanity.com/paper/2507.11136/) (2025)
- [Scalable Bayesian Tensor Ring Factorization for Multiway Data Analysis](https://mlsanity.com/paper/2412.03321/) (2024)
- [Variational Bayesian inference for CP tensor completion with side information](https://mlsanity.com/paper/2206.12486/) (2022)
- [Tensor Shape Search for Optimum Data Compression](https://mlsanity.com/paper/2205.10651/) (2022)
- [Unsupervised feature selection using Bayesian Tucker decomposition](https://mlsanity.com/paper/2604.14949/) (2026)

## Abstract (arXiv)

Tucker decomposition is the cornerstone of modern machine learning on tensorial data analysis, which have attracted considerable attention for multiway feature extraction, compressive sensing, and tensor completion. The most challenging problem is related to determination of model complexity (i.e., multilinear rank), especially when noise and missing data are present. In addition, existing methods cannot take into account uncertainty information of latent factors, resulting in low generalization performance. To address these issues, we present a class of probabilistic generative Tucker models for tensor decomposition and completion with structural sparsity over multilinear latent space. To exploit structural sparse modeling, we introduce two group sparsity inducing priors by hierarchial representation of Laplace and Student-t distributions, which facilitates fully posterior inference. For model learning, we derived variational Bayesian inferences over all model (hyper)parameters, and developed efficient and scalable algorithms based on multilinear operations. Our methods can automatically adapt model complexity and infer an optimal multilinear rank by the principle of maximum lower bound of model evidence. Experimental results and comparisons on synthetic, chemometrics and neuroimaging data demonstrate remarkable performance of our models for recovering ground-truth of multilinear rank and missing entries.