In order to address privacy concerns, many social media websites allow users to hide their personal profiles from the public. In this work, we show how an adversary can exploit a social network with a mixture of public and private user profiles to predict the private attributes of users. We map this problem to a relational classification problem and we propose a simple yet powerful model that uses group features and group memberships of users to perform multi-value classification. We compare its efficacy against several other classification approaches. Our results show that even in the case when there is an option for making profile attributes private, if links and group affiliations are known, users' privacy in social networks may be compromised. On a dataset from a well-known social-media website, we could easily recover the sensitive attributes for half of the private-profile users with a high accuracy when as much as half of the profiles are private. To the best of our knowledge, this is the first work that uses link-based and group-based classification to study privacy implications in social networks. We conclude with a discussion of our findings and the broader applicability of our proposed model.