For the minimum symbol error, the marginal (and posterior) probability p m (g|w N 1 ) has to be computed: which, due to the specific structure of the model p(g n |g n−1 n−2 , w n+2 n−2 ), can be calculated efficiently using only a forward algorithm (without a 'backward' part).
we obtain the decision rule for minimum symbol error at positions m = 1, ..., N : As in the case of the generative model, the computational effort is to compute the posterior probability p m (g|w N 1 ) rather than to find the most probable tag at position m. So far, we have said nothing about how we train the free parameters of the model distributions.