Growth transformations for probabilistic functions of stochastic grammars

Stochastic Grammars are the most usual models in Syntactic Pattern Recognition. Both components of a Stochastic Grammar, the characteristic grammar and the probabilities attached to the rules, can be learnt automatically from training samples. In this paper, first a review of some algorithms are presented to infer the probabilistic component of Stochastic Regular and Context-Free Grammars under the framework of the Growth Transformations. On the other hand, with Stochastic Grammars, the patterns must be represented as strings over a finite set of symbols. However, the most natural representation in many Syntactic Pattern Recognition applications (i.e. speech) is as sequences of vectors from a feature vector space, that is, a continuous representation. Therefore, to obtain a discrete representation of the patterns, some quantization errors are introduced in the representation process. To avoid this drawback, a formal presentation of a semi-continuous extension of the Stochastic Regular and Context-Free Grammars is studied and probabilistic estimation algorithms are developed in this paper. In this extension, sequences of vectors, instead of strings of symbols, can be processed with Stochastic Grammars.