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Parsing and translating natural languages can be viewed as problems of predicting tree structures. For machine learning approaches to these predictions, the diversity and high dimensionality of the structures involved mandate very large training sets. This paper presents a purely discriminative learning method that scales up well to problems of this size. Its accuracy was at least as good as other comparable methods on a standard parsing task. To our knowledge, it is the first purely discriminative learning algorithm for translation with treestructured models. Unlike other popular methods, this method does not require a great deal of feature engineering a priori, because it performs feature selection over a compound feature space as it learns. Experiments demonstrate the method's versatility, accuracy, and efficiency. Relevant software is freely available at http://nlp.cs.nyu.edu/parser and http://nlp.cs.nyu.edu/GenPar.