Previous work (Seginer, 2007;Ponvert et al., 2011;Shain et al., 2016;Jin et al., 2018b) show that using data likelihood as both the objective for optimization and the criterion for model selection, either implicitly (in the case of Bayesian models) or explicitly (in the case of EM), gives good results on grammar induction.
it is also known that data likelihood is only weakly correlated with parsing accuracy, especially at convergence (Smith, 2006;Johnson et al., 2007;Jin et al., 2018a).