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We study the problem of medical symptoms recognition from patient text, for the purposes of gathering pertinent information from the patient (known as history-taking). A typical patient text is often descriptive of the symptoms the patient is experiencing and a single instance of such a text can be "labeled" with multiple symptoms. This makes learning a medical symptoms recognizer challenging on account of i) the lack of availability of voluminous annotated data as well as ii) the large unknown universe of multiple symptoms that a single text can map to. Furthermore, patient text is often characterized by a long tail in the data (i.e., some labels/symptoms occur more frequently than others for e.g "fever" vs "hematochezia"). In this paper, we introduce an active learning method that leverages underlying structure of a continually refined, learned latent space to select the most informative examples to label. This enables the selection of the most informative examples that progressively increases the coverage on the universe of symptoms via the learned model, despite the long tail in data distribution.