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This paper presents a new method for inferring the semantic properties of documents by leveraging free-text keyphrase annotations. Such annotations are becoming increasingly abundant due to the recent dramatic growth in semi-structured, user-generated online content. One especially relevant domain is product reviews, which are often annotated by their authors with pros/cons keyphrases such as ``a real bargain'' or ``good value.'' These annotations are representative of the underlying semantic properties; however, unlike expert annotations, they are noisy: lay authors may use different labels to denote the same property, and some labels may be missing. To learn using such noisy annotations, we find a hidden paraphrase structure which clusters the keyphrases. The paraphrase structure is linked with a latent topic model of the review texts, enabling the system to predict the properties of unannotated documents and to effectively aggregate the semantic properties of multiple reviews. Our approach is implemented as a hierarchical Bayesian model with joint inference. We find that joint inference increases the robustness of the keyphrase clustering and encourages the latent topics to correlate with semantically meaningful properties. Multiple evaluations demonstrate that our model substantially outperforms alternative approaches for summarizing single and multiple documents into a set of semantically salient keyphrases.