We describe a framework for inducing probabilistic grammars from corpora of positive samples. First, samples are incorporated by adding ad-hoc rules to a working grammar; subsequently, elements of the model (such as states or nonterminals) are merged to achieve generalization and a more compact representation. The choice of what to merge and when to stop is governed by the Bayesian posterior probability of the grammar given the data, which formalizes a trade-off between a close fit to the data and a default preference for simpler models ('Occam's Razor'). The general scheme is illustrated using three types of probabilistic grammars: Hidden Markov models, class-based ¢ -grams, and stochastic context-free grammars.

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