DFKI, DFKI Research Reports (RR), Vol. 01-02, 2001.
It is an interesting fact that most of the stochastic models used by linguists can be interpreted as probabilistic context-free grammars. In this paper, this result will be accompanied by the formal proof that the inside-outside algorithm, the standard training method for probabilistic context-free grammars, can be regarded as a dynamic-programming variant of the EM algorithm. Even if this result is considered in isolation this means that most of the probabilistic models used by linguists are trained by a version of the EM algorithm. However, this result is even more interesting when considered in a theoretical context because the well-known convergence behavior of the inside-outside algorithm has been confirmed by many experiments but it seems that it never has been formally proved. Furthermore, being a version of the EM algorithm, the inside-outside algorithm also inherits the good convergence behavior of EM. We therefore contend that the as yet imperfect line of argumentation can be transformed into a coherent proof.