They use aligned sequences of words, called biphrases, as building blocks for translations, and score alternative candidate translations for the same source sentence based on a log-linear model of the conditional probability of target sentences given the source sentence:

alignment a, where the alignment is a representation of the sequence of biphrases that where used in order to build T from S; The Ak’s are weights and ZS is a normalization factor that guarantees that p is a proper conditional probability distribution over the pairs (T, A).

These typically include forward and reverse phrase conditional probability features log p(f|§) as well as logp(§ where 59' is the source side of the biphrase and f the target side, and the so-called “phrase penalty” and “word penalty” features, which count the number of phrases and words in the alignment.

For example, in the example of Figure 3, the cost of this - machine translation - is - strange, can only take into account the conditional probability of the word strange relative to the word is, but not relative to the words translation and is.

its translation has larger conditional probability ) or because the associated heuristics is less tight, hence more optimistic.

The joint probability is expressed as a chain product of a series of conditional probabilities of token pairs P({ei}, {cj}) = P((ék,ck)|(ék_1,ck_1)), k = 1 .

The conditional probabilities for token pairs are estimated from the aligned training corpus.

From the affinity matrix conditional probabilities P(ei|cj) can be estimated as

We estimate conditional probability of Chinese phoneme cpk, after observing English character 6, as

We apply CRFs as our base learner throughout this paper and employ a utility function which is based on the conditional probability of the most likely label sequence 37* for an observation sequence :8 (cf.

See Equation (1) for the conditional probability PX(37 with ZX calculated as in Equation (6).

The marginal and conditional probabilities are used by our AL approaches as confidence estimators.

Then we apply the EM algorithm (Dempster et al., 1977) to estimate the conditional probabilities P(f|z), and P(z|v) with respect to each dependence in Figure 3 as follows.

o M-Step: re-estimates conditional probabilities P(zk|vi) and P(zk|wl):

and conditional probability P(fj |zk), which is a mixture portion of posterior probability of latent variables