Bayesian non-parametric non-negative matrix factorization for pattern identification in environmental mixtures

Environmental health researchers may aim to identify exposure patterns that represent sources, product use, or behaviors that give rise to mixtures of potentially harmful environmental chemical exposures. We present Bayesian non-parametric non-negative matrix factorization (BN^2MF) as a novel method to identify patterns of chemical exposures when the number of patterns is not known a priori. We placed non-negative continuous priors on pattern loadings and individual scores to enhance interpretability and used a clever non-parametric sparse prior to estimate the pattern number. We further derived variational confidence intervals around estimates; this is a critical development because it quantifies the model's confidence in estimated patterns. These unique features contrast with existing pattern recognition methods employed in this field which are limited by user-specified pattern number, lack of interpretability of patterns in terms of human understanding, and lack of uncertainty quantification.