Smooth and Probabilistic PARAFAC Model with Auxiliary Covariates

As immunological and clinical studies become more complex, there is an increasing need to analyze temporal immunophenotypes alongside demographic and clinical covariates, where each subject receives matrix-valued time series observations for potentially high-dimensional longitudinal features, as well as other static characterizations. Researchers aim to find the low-dimensional embedding of subjects using matrix-valued time series observations and investigate relationships between static clinical responses and the embedding. However, constructing these embeddings can be challenging due to high dimensionality, sparsity, and irregularity in sample collection over time. In addition, the incorporation of static auxiliary covariates is frequently desired during such a construction. To address these issues, we propose a smoothed probabilistic PARAFAC model with covariates (SPACO) that uses auxiliary covariates of interest. We provide extensive simulations to test different aspects of SPACO and demonstrate its application to an immunological dataset from patients with SARS-CoV-2 infection. Supplementary materials for this article are available online.