Expressing the lattice model in log-linear form, we can write the marginal probability P (x) of a given sentence x as: for y i,j = s, y i,j+1 = s , and Computationally, the lattice MRF is preferable to a naïve Factorial HMM (Ghahramani and Jordan, 1997) representation, which would require O(2 M ) parameters for an M -layer model.
we use an open source Conditional Random Field (CRF) (Lafferty et al., 2001) software package 4 designed by Sunita Sarawagi and william w. Cohen to implement our supervised models.