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Learning to predict rare events from sequences of events with categorical features is an important, real-world, problem that existing statistical and machine learning methods are not well suited to solve. This paper describes timeweaver, a genetic algorithm based machine learning system that predicts rare events by identifying predictive temporal and sequential patterns. Timeweaver is applied to the task of predicting telecommunication equipment failures from 110,000 alarm messages and is shown to outperform existing learning methods.