Consistency of stochastic context-free grammars from probabilistic estimation based on growth transformations

An important problem related to the probabilistic estimation of stochastic context-free grammars (SCFGs) is guaranteeing the consistency of the estimated model. This problem was considered by Booth-Thompson (1973) and Wetherell (1980) and studied by Maryanski (1974) and Chaudhuri et al. (1983) for unambiguous SCFGs only, when the probability distributions were estimated by the relative frequencies in a training sample. In this work, we extend this result by proving that the property of consistency is guaranteed for all SCFGs without restrictions, when the probability distributions are learned from the classical inside-outside and Viterbi algorithms, both of which are based on growth transformations. Other important probabilistic properties which are related to these results are also proven