We propose a non-parametric approach for characterizing heterogeneous diseases in large-scale studies. We target diseases where multiple types of pathology present simultaneously in each subject and a more severe disease manifests as a higher level of tissue destruction. For each subject, we model theof local image descriptors as samples generated by an unknown subject-specific probability density. Instead of approximating the probability density via a parametric family, we propose to side step the parametric inference by directly estimating the divergence between subject densities. Our method maps the collection of local image descriptors to a signaturethat is used to predict a clinical measurement. We are able to interpret the prediction of the clinical variable in the population and individual levels by carefully studying the divergences. We illustrate an application this method on simulated data as well as on a large-scale lung CT study of Chronic Obstructive Pulmonary Disease (COPD). Our approach outperforms classical methods on both simulated and COPD data and demonstrates the state-of-the-art prediction on an important physiologic measure of airflow (the forced respiratory volume in one second, FEV1).