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We develop a Bayesian approach to predict a continuous or binary outcome fromdata that are collected from multiple sources with a multi-way (i.e..multidimensional tensor) structure. As a motivating example we considermolecular data from multiple 'omics sources, each measured over multipledevelopmental time points, as predictors of early-life iron deficiency (ID) ina rhesus monkey model. We use a linear model with a low-rank structure on thecoefficients to capture multi-way dependence and model the variance of thecoefficients separately across each source to infer their relativecontributions. Conjugate priors facilitate an efficient Gibbs samplingalgorithm for posterior inference, assuming a continuous outcome with normalerrors or a binary outcome with a probit link. Simulations demonstrate that ourmodel performs as expected in terms of misclassification rates and correlationof estimated coefficients with true coefficients, with large gains inperformance by incorporating multi-way structure and modest gains whenaccounting for differing signal sizes across the different sources. Moreover,it provides robust classification of ID monkeys for our motivating application.Software in the form of R code is available athttps://github.com/BiostatsKim/BayesMSMW .

Bayesian predictive modeling of multi-source multi-way data