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We consider the task of suggesting related queries to users after they issue their initial query to a web search engine. We propose a machine learning approach to learn the probability that a user may find a follow-up query both useful and relevant, given his initial query. Our approach is based on a machine learning model which enables us to generalize to queries that have never occurred in the logs as well. The model is trained on co-occurrences mined from the search logs, with novel utility and relevance models, and the machine learning step is done without any labeled data by human judges. The learning step allows us to generalize from the past observations and generate query suggestions that are beyond the past co-occurred queries. This brings significant gains in coverage while yielding modest gains in relevance. Both offline (based on human judges) and online (based on millions of user interactions) evaluations demonstrate that our approach significantly outperforms strong baselines.