Consistency of Stochastic Context-Free Grammars From Probabilistic Estimation Based on Growth Transformations
Issue No. 09 - September (1997 vol. 19)
DOI Bookmark: http://doi.ieeecomputersociety.org/10.1109/34.615455
<p><b>Abstract</b>—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 in [<ref rid="bibi10523" type="bib">3</ref>], [<ref rid="bibi105214" type="bib">14</ref>] and studied in [<ref rid="bibi105210" type="bib">10</ref>], [<ref rid="bibi10524" type="bib">4</ref>] for unambiguous SCFGs only, when the probabilistic 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.</p>
Stochastic context-free grammar, consistency, probabilistic estimation, inside-outside algorithm, growth transformations.
Joan-Andreu Sánchez, José-Miguel Benedí, "Consistency of Stochastic Context-Free Grammars From Probabilistic Estimation Based on Growth Transformations", IEEE Transactions on Pattern Analysis & Machine Intelligence, vol. 19, no. , pp. 1052-1055, September 1997, doi:10.1109/34.615455