Generalization errors in estimation of stochastic context-free grammar

In sequential data analysis, such as natural language processing and gene analysis, stochastic context-free grammars are commonly used. In spite of the wide-ranged applications and many learning algorithms, the theoretical 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 performance 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 structure.