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Proceedings of the main conference on Human Language Technology Conference of the North American Chapter of the Association of Computational Linguistics -
We investigate the problem of training probabilistic context-free grammars on the basis of a distribution defined over an infinite set of trees, by minimizing the cross-entropy. This problem can be seen as a generalization of the well-known maximum likelihood estimator on (finite) tree banks. We prove an unexpected theoretical property of grammars that are trained in this way, namely, we show that the derivational entropy of the grammar takes the same value as the crossentropy between the inputdoi:10.3115/1220835.1220878 fatcat:hwkh2td7cnewjnnridn7e4pstu