On the other hand, estimating the parameters under Maximum-Likelihood Estimation (MLE) for the latent translation structure model p(σ) is bound to overfit towards memorising whole sentence-pairs as discussed in (Mylonakis and Sima'an, 2010), with the resulting grammar estimate not being able to generalise past the training data.
apart from overfitting towards long phrase-pairs, a grammar with millions of structural rules is also liable to overfit towards degenerate latent structures which, while fitting the training data well, have limited applicability to unseen sentences.