BAMITA: Bayesian multiple imputation for tensor arrays

Area of Science:

• Biomedical data science
• Statistical modeling
• Computational biology

Background:

• Biomedical data often form multi-way arrays (tensors) and are frequently incomplete.
• Existing tensor imputation methods provide point estimates but fail to capture uncertainty.
• Longitudinal microbiome studies are a key application area with missing time-point data.

Purpose of the Study:

• To develop a novel multiple imputation method for incomplete tensors within a Bayesian framework.
• To address the limitation of existing methods by incorporating uncertainty quantification.
• To enable more robust downstream analyses of biomedical tensor data.

Main Methods:

• A flexible Bayesian framework utilizing multiple imputation for tensor data.
• Application of conjugate priors for CANDECOMP/PARAFAC (CP) factorization.
• Incorporation of a separable residual covariance structure for efficient modeling.

Main Results:

• The proposed method demonstrates high accuracy in imputing missing tensor entries, including entire fibers.
• Effective uncertainty calibration is achieved, providing realistic estimates of missing data variability.
• The approach performs well in scenarios with both single-entry and fiber-wise missing data.

Conclusions:

• The Bayesian multiple imputation approach offers a significant advancement for handling incomplete biomedical tensor data.
• Accurate imputation and uncertainty quantification are crucial for reliable analysis of microbiome and other biomedical datasets.
• The method facilitates robust inference on population-level trends, such as species diversity in microbiome studies.