Most automatic text summarization systems proposed to date rely on centrality and structural features as indicators for information importance. In this paper, we argue that these features cannot reliably detect important information in heterogeneous document collections. Instead, we propose CPSum, a summarizer that learns the importance of information objects from a background source. Our hypothesis is tested on multi-document corpora with removed centrality and structural features. CPSum shows to be able to perform well in these corpora whereas reference systems fail.