Standard statistical models of language fail to capture one of the most striking properties of natural languages: the power-law distribution in the frequencies of word tokens. We present a framework for developing statistical models that generically produce power-laws, augmenting standard generative models with an adaptor that produces the appropriate pattern of token frequencies. We show that taking a particular stochastic process - the Pitman-Yor process - as an adaptor justifies the appearance of type frequencies in formal analyses of natural language, and improves the performance of a model for unsupervised learning of morphology.
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