# BAMITA: Bayesian Multiple Imputation for Tensor Arrays

arXiv: https://arxiv.org/abs/2410.23412 · HTML: https://mlsanity.com/paper/2410.23412/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 6 of its 24 references that are in the map.
- First posted on arXiv 30 Oct 2024.

## Builds on (most cited first, 6 of 6)

- [Smooth PARAFAC Decomposition for Tensor Completion](https://mlsanity.com/paper/1505.06611/) (2015)
- [Multilinear tensor regression for longitudinal relational data](https://mlsanity.com/paper/1412.0048/) (2014)
- [Bayesian Tensor Regression](https://mlsanity.com/paper/1509.06490/) (2015)
- [Sparse Bayesian Factor Analysis when the Number of Factors is Unknown](https://mlsanity.com/paper/1804.04231/) (2018)
- [Bayesian Tensor-on-Tensor Regression with Efficient Computation](https://mlsanity.com/paper/2210.11363/) (2022)
- [Smooth and probabilistic PARAFAC model with auxiliary covariates](https://mlsanity.com/paper/2104.05184/) (2021)

## Abstract (arXiv)

Data increasingly take the form of a multi-way array, or tensor, in several biomedical domains. Such tensors are often incompletely observed. For example, we are motivated by longitudinal microbiome studies in which several timepoints are missing for several subjects. There is a growing literature on missing data imputation for tensors. However, existing methods give a point estimate for missing values without capturing uncertainty. We propose a multiple imputation approach for tensors in a flexible Bayesian framework, that yields realistic simulated values for missing entries and can propagate uncertainty through subsequent analyses. Our model uses efficient and widely applicable conjugate priors for a CANDECOMP/PARAFAC (CP) factorization, with a separable residual covariance structure. This approach is shown to perform well with respect to both imputation accuracy and uncertainty calibration, for scenarios in which either single entries or entire fibers of the tensor are missing. For two microbiome applications, it is shown to accurately capture uncertainty in the full microbiome profile at missing timepoints and used to infer trends in species diversity for the population. Documented R code to perform our multiple imputation approach is available at https://github.com/lockEF/MultiwayImputation .