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With increasing studies in identifying pathology-induced group differences between patients and controls, there is also a growing need to simultaneously analyze multiple clinical measures, to elucidate group differences. In this paper, we present a novel learning-based method that uses Bayesian networks (BN) to model the inter-relationship between multiple clinical measures on facial expressions, for the study of emotional impairments in schizophrenia. Such measures include universal emotion states, and associated facial actions that are encoded by action units (AUs) (Ekman and Friesen, 1978). Characterizing the relationship between emotions and facial actions can describe subtle facial expressions, thus helping the identification of emotional impairments in schizophrenia. We introduce a three-layered BN model to represent facial expressions, and then present an iterative algorithm to learn the BN structure by categorizing AUs into different sets, based on their impact on characterizing emotions. The learned BN can be used for a qualitative structure-based comparison between patients and controls, and also for quantitative measurements of emotional impairments. Experiments on real data sets demonstrate that our method can identify underlying differences between patients and controls, and hence is able to validate clinical hypotheses, and to aid diagnosis of schizophrenia.