In order to encourage sparse grammars and avoid overfitting, recent research for training PCFGs has drifted away from MLE in favor of Bayesian inference algorithms that make either deterministic or stochastic approximations (Kurihara and Sato, 2006;Johnson et al., 2006;Johnson et al., 2007).
mCmC algorithms improves the performance over Em and VB at the cost of much more training time.