Viterbi Training for PCFGs: Hardness Results and Competitiveness of Uniform Initialization

We consider the search for a maximum likelihood assignment of hidden derivations and grammar weights for a probabilistic context-free grammar, the problem approximately solved by “Viterbi training.” We show that solving and even approximating Viterbi training for PCFGs is NP-hard. We motivate the use of uniformat-random initialization for Viterbi EM as an optimal initializer in absence of further information about the correct model parameters, providing an approximate bound on the log-likelihood.