Inside-outside estimation meets dynamic EM : gold

Abstract

It is an interesting fact that most of the stochastic models used by linguists can be interpreted as probabilistic context-free grammars (Prescher 2001). 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 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 yet imperfect line of argumentation can be transformed into a coherent proof.