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We present our system for the Interspeech 2013 Computational Paralinguistics Autism Sub-challenge. Our contribution focuses on improving classification accuracy of developmental disorders by applying a novel feature selection technique to the rich set of acoustic-prosodic features provided for this purpose. Our feature selection approach is based on submodular function optimization. We demonstrate significant improvements over systems using the full feature set and over a standard feature selection approach. Our final system outperforms the official Challenge baseline system significantly on the development set for both classification tasks, and on the test set for the Typicality task. Finally, we analyze the subselected features and identify the most important ones.