  We develop a hierarchical infinite latent factor model (HIFM) to
appropriately account for the covariance structure across subpopulations in
data. We propose a novel Hierarchical Dirichlet Process shrinkage prior on the
loadings matrix that flexibly captures the underlying structure of our data
across subpopulations while sharing information to improve inference and
prediction. The stick-breaking construction of the prior assumes infinite
number of factors and allows for each subpopulation to utilize different
subsets of the factor space and select the number of factors needed to best
explain the variation. Theoretical results are provided to show support of the
prior. We develop the model into a latent factor regression method that excels
at prediction and inference of regression coefficients. Simulations are used to
validate this strong performance compared to baseline methods. We apply this
work to the problem of predicting surgical complications using electronic
health record data for geriatric patients at Duke University Health System
(DUHS). We utilize additional surgical encounters at DUHS to enhance learning
for the targeted patients. Using HIFM to identify high risk patients improves
the sensitivity of predicting death to 91% from 35% based on the currently used
heuristic.
