We aim at finding the comorbidity patterns of substance abuse, mood and personality disorders using the diagnoses from the National Epidemiologic Survey on Alcohol and Related Conditions database. To this end, we propose a novel Bayesian nonparametric latent feature model for categorical observations, based on the Indian buffet process, in which the latent variables can take values between 0 and 1. The proposed model has several interesting features for modeling psychiatric disorders. First, the latent features might be off, which allows distinguishing between the subjects who suffer a condition and those who do not. Second, the active latent features take positive values, which allows modeling the extent to which the patient has that condition. We also develop a new Markov chain Monte Carlo inference algorithm for our model that makes use of a nested expectation propagation procedure.

An iterative reweighted least squares (IRWLS) procedure recently proposed is shown to converge to the support vector machine solution. The convergence to a stationary point is ensured by modifying the original IRWLS procedure.