  The analysis of comorbidity is an open and complex research field in the
branch of psychiatry, where clinical experience and several studies suggest
that the relation among the psychiatric disorders may have etiological and
treatment implications. In this paper, we are interested in applying latent
feature modeling to find the latent structure behind the psychiatric disorders
that can help to examine and explain the relationships among them. To this end,
we use the large amount of information collected in the National Epidemiologic
Survey on Alcohol and Related Conditions (NESARC) database and propose to model
these data using a nonparametric latent model based on the Indian Buffet
Process (IBP). Due to the discrete nature of the data, we first need to adapt
the observation model for discrete random variables. We propose a generative
model in which the observations are drawn from a multinomial-logit distribution
given the IBP matrix. The implementation of an efficient Gibbs sampler is
accomplished using the Laplace approximation, which allows integrating out the
weighting factors of the multinomial-logit likelihood model. We also provide a
variational inference algorithm for this model, which provides a complementary
(and less expensive in terms of computational complexity) alternative to the
Gibbs sampler allowing us to deal with a larger number of data. Finally, we use
the model to analyze comorbidity among the psychiatric disorders diagnosed by
experts from the NESARC database.
