In this paper, we tackle the issue of symptom recognition for rare diseases in biomedical texts. Symptoms typically have more complex and ambiguous structure than other biomedical named entities. Furthermore , existing resources are scarce and incomplete. Therefore, we propose a weakly-supervised framework based on a combination of two approaches: sequential pattern mining under constraints and sequence labeling. We use unannotated biomedical paper abstracts with dictionaries of rare diseases and symptoms to create our training data. Our experiments show that both approaches outperform simple projection of the dictionaries on text, and their combination is beneficial. We also introduce a novel pattern mining constraint based on semantic similarity between words inside patterns.