Using WFSTs for Efficient EM Learning of Probabilistic CFGs and Their Extensions

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  • Kameya Yoshitaka
    Department of Computer Science, Graduate School of Information Science and Engineering, Tokyo Institute of Technology
  • Mori Takashi
    Department of Computer Science, Graduate School of Information Science and Engineering, Tokyo Institute of Technology
  • Sato Taisuke
    Department of Computer Science, Graduate School of Information Science and Engineering, Tokyo Institute of Technology

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Abstract

Probabilistic context-free grammars (PCFGs) are a widely known class of probabilistic language models. The Inside-Outside (I-O) algorithm is well known as an efficient EM algorithm tailored for PCFGs. Although the algorithm requires inexpensive linguistic resources, there remains a problem in its efficiency. This paper presents an efficient method for training PCFG parameters in which the parser is separated from the EM algorithm, assuming that the underlying CFG is given. A new EM algorithm exploits the compactness of well-formed substring tables (WFSTs) generated by the parser. Our proposal is general in that the input grammar need not take Chomsky normal form (CNF) while it is equivalent to the I-O algorithm in the CNF case. In addition, we propose a polynomial-time EM algorithm for CFGs with context-sensitive probabilities, and report experimental results with the ATR dialogue corpus and a hand-crafted Japanese grammar.

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