  We propose a categorical matrix factorization method to infer latent diseases
from electronic health records (EHR) data in an unsupervised manner. A latent
disease is defined as an unknown biological aberration that causes a set of
common symptoms for a group of patients. The proposed approach is based on a
novel double feature allocation model which simultaneously allocates features
to the rows and the columns of a categorical matrix. Using a Bayesian approach,
available prior information on known diseases greatly improves identifiability
and interpretability of latent diseases. This includes known diagnoses for
patients and known association of diseases with symptoms. We validate the
proposed approach by simulation studies including mis-specified models and
comparison with sparse latent factor models. In the application to Chinese EHR
data, we find interesting results, some of which agree with related clinical
and medical knowledge.
