# Bayesian Conditional Tensor Factorizations for High-Dimensional Classification

arXiv: https://arxiv.org/abs/1301.4950 · HTML: https://mlsanity.com/paper/1301.4950/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 21 Jan 2013.

## Built on by (most cited first, 6 of 6)

- [Nonparametric Sparse Tensor Factorization with Hierarchical Gamma Processes](https://mlsanity.com/paper/2110.10082/) (2021)
- [Streaming Factor Trajectory Learning for Temporal Tensor Decomposition](https://mlsanity.com/paper/2310.17021/) (2023)
- [Nonparametric Embeddings of Sparse High-Order Interaction Events](https://mlsanity.com/paper/2207.03639/) (2022)
- [Dynamic Tensor Decomposition via Neural Diffusion-Reaction Processes](https://mlsanity.com/paper/2310.19666/) (2023)
- [Interpretable Bayesian Tensor Network Kernel Machines with Automatic Rank and Feature Selection](https://mlsanity.com/paper/2507.11136/) (2025)
- [Joint Bayesian Parameter and Model Order Estimation for Low-Rank Probability Mass Tensors](https://mlsanity.com/paper/2410.06329/) (2024)

## Abstract (arXiv)

In many application areas, data are collected on a categorical response and high-dimensional categorical predictors, with the goals being to build a parsimonious model for classification while doing inferences on the important predictors. In settings such as genomics, there can be complex interactions among the predictors. By using a carefully-structured Tucker factorization, we define a model that can characterize any conditional probability, while facilitating variable selection and modeling of higher-order interactions. Following a Bayesian approach, we propose a Markov chain Monte Carlo algorithm for posterior computation accommodating uncertainty in the predictors to be included. Under near sparsity assumptions, the posterior distribution for the conditional probability is shown to achieve close to the parametric rate of contraction even in ultra high-dimensional settings. The methods are illustrated using simulation examples and biomedical applications.