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Probabilistic topic models, have been widely deployed for various applications such as learning disease or tissue subtypes. Yet, learning the parameters of such models is usually an ill-posed problem and may result in losing valuable information about disease severity. A common approach is to add a discriminative loss term to the generative model’s loss in order to learn a representation that is also predictive of disease severity. However, finding a balance between these two losses is not straightforward. We propose an alternative way in this paper. We develop a framework which allows for incorporating external covariates into the generative model’s approximate posterior. These covariates can have more discriminative power for disease severity compared to the representation that we extract from the posterior distribution. For instance, they can be features extracted from a neural network which predicts disease severity from CT images. Effectively, we enforce the generative model’s approximate posterior to reside in the subspace of these discriminative covariates. We illustrate our method’s application on a large-scale lung CT study of Chronic Obstructive Pulmonary Disease (COPD), a highly heterogeneous disease. We aim at identifying tissue subtypes by using a variant of topic model as a generative model. We quantitatively evaluate the predictive performance of the inferred subtypes and demonstrate that our method outperforms or performs on par with some reasonable baselines. We also show that some of the discovered subtypes are correlated with genetic measurements, suggesting that the identified subtypes may characterize the disease’s underlying etiology.