Smooth and probabilistic PARAFAC model with auxiliary covariates

TL;DR

The paper introduces SPACO, a novel smoothed probabilistic PARAFAC model that effectively handles high-dimensional, sparse, and irregular longitudinal data while incorporating auxiliary covariates, demonstrated through simulations and COVID-19 immunological data.

Contribution

It develops a new SPACO model that combines smoothing, probabilistic PARAFAC, and covariate integration for complex longitudinal data analysis.

Findings

SPACO outperforms existing methods in simulations.

Effective in handling sparse and irregular data.

Demonstrated utility on COVID-19 immunological data.

Abstract

In immunological and clinical studies, matrix-valued time-series data clustering is increasingly popular. Researchers are interested in finding low-dimensional embedding of subjects based on potentially high-dimensional longitudinal features and investigating relationships between static clinical covariates and the embedding. These studies are often challenging due to high dimensionality, as well as the sparse and irregular nature of sample collection along the time dimension. We propose a smoothed probabilistic PARAFAC model with covariates (SPACO) to tackle these two problems while utilizing auxiliary covariates of interest. We provide intensive simulations to test different aspects of SPACO and demonstrate its use on an immunological data set from patients with SARs-CoV-2 infection.