In other words, the model tries to maximize: Since the correct hybrid tree associated with n-m pair is unknown, we marginalize over the hidden variable h. The model parameters will then be estimated using the Expectation-Maximization (EM) algorithm (Dempster et al., 1977).
an inside-outside style algorithm (Baker, 2005) is used where an additional layer of dynamic programming algorithms are used for efficient inference (Lu et al., 2008).