Generalization Errors in Estimation of Stochastic Context-Free Grammar

K. Yamazaki and S. Watanabe (Japan)


Artiﬁcial intelligence, Machine learning, Statistical learn ing machine, Stochastic context-free grammar, Bayesian generalization error, Algebraic geometry


In sequential data analysis, such as natural language pro cessing and gene analysis, stochastic context-free gram mars are commonly used. In spite of the wide-ranged applications and many learning algorithms, the theoreti cal properties have not been clariﬁed. When the grammar is parametrized, we can regard the production system of words with the grammar as a statistical learning machine, which falls into a singular machine. In this paper, the per formance of the system is revealed based on the algebraic geometrical method, which enables us to analyze singular machines. The result helps to estimate the grammar struc ture.

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