Assuming as in Och (2003) that error count is additively decomposable by sentence-i.e., E(r S 1 , e S 1 ) = s E(r s , e s )-this results in the following optimization problem: 2 The quality of this approximation is dependent on how accurately the N -best lists represent the search space of the system.
the hypothesis list is iteratively grown: decoding with an initial parameter vector seeds the N -best lists; next, parameter estimation and N -best list gathering alternate until the search space is deemed representative.