BAMITA: Bayesian Multiple Imputation for Tensor Arrays

Area of Science:

• Biomedical data science
• Computational biology
• Statistical modeling

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 flexible Bayesian multiple imputation framework for incomplete tensor data.
• To accurately simulate missing values and propagate uncertainty in subsequent analyses.
• To address limitations of existing methods by providing uncertainty quantification.

Main Methods:

• A Bayesian multiple imputation approach using a CANDECOMP/PARAFAC (CP) factorization.
• Incorporation of conjugate priors and a separable residual covariance structure.
• Application to scenarios with missing single entries or entire tensor fibers.

Main Results:

• The proposed method demonstrates strong performance in both imputation accuracy and uncertainty calibration.
• It effectively handles missing data in single entries and entire fibers of tensors.
• Accurate uncertainty capture for microbiome profiles at missing timepoints was achieved.

Conclusions:

• The Bayesian multiple imputation framework offers a robust solution for incomplete tensor data in biomedical research.
• It enables more reliable downstream analyses by accounting for imputation uncertainty.
• The method is particularly valuable for longitudinal microbiome studies and inferring population-level trends.