Automated music playlist generation is a specific form of music recommendation. Generally stated, the user receives a set of song suggestions defining a coherent listening session. We hypothesize that the best way to convey such playlist coherence to new recommendations is by learning it from actual curated examples, in contrast to imposing ad hoc constraints. Collaborative filtering methods can be used to capture underlying patterns in hand-curated playlists. However, the scarcity of thoroughly curated playlists and the bias towards popular songs result in the vast majority of songs occurring in very few playlists and thus being poorly recommended. To overcome this issue, we propose an alternative model based on a song-to-playlist classifier, which learns the underlying structure from actual playlists while leveraging song features derived from audio, social tags and independent listening logs. Experiments on two datasets of hand-curated playlists show competitive performance compared to collaborative filtering when sufficient training data is available and more robust performance when recommending rare and out-of-set songs. For example, both approaches achieve a recall@100 of roughly 35% for songs occurring in 5 or more training playists, whereas the proposed model achieves a recall@100 of roughly 15% for songs occurring in 4 or less training playlists, compared to the 3% achieved by collaborative filtering.