Un-igrams are produced by lexical rules, while higher-order n-grams can be produced either directly by lexical rules, or by combining constituents.

The n-gram language model score of e similarly decomposes over the h in e that produce n-grams .

The linear similarity measure takes the following form, where Tn is the set of n-grams:

Above, we compare the precision, relative to reference translations, of sets of n-grams chosen in two ways.

The left bar is the precision of the n-grams in 6*.

The right bar is the precision of n-grams with E[c(6, 75)] > p. To justify this comparison, we chose p so that both methods of choosing 71- grams gave the same n-gram recall: the fraction of n-grams in reference translations that also appeared in 6* or had E[6(6, 75)] > p.

This linear function contains n + 1 parameters 60, 61, ..., 6 N, where N is the maximum order of the n-grams involved.

First, the set of n-grams is extracted from the lattice.

For a moderately large lattice, there can be several thousands of n-grams and the procedure becomes expensive.

For each node 75 in the lattice, we maintain a quantity Score(w, t) for each n-gram 212 that lies on a path from the source node to t. Score(w, t) is the highest posterior probability among all edges on the paths that terminate on t and contain n-gram w. The forward pass requires computing the n-grams introduced by each edge; to do this, we propagate n-grams (up to maximum order — l) terminating on each node.

Here we do not discriminate among different lexical n-grams and are only concerned with statistics aggregation of all n-grams of the same order.

Gn+(e,e') is the n-gram agreement measure function which counts the number of occurrences in e'of n-grams in 6.

So the corresponding feature value will be the expected number of occurrences in 17-[k (f) of all n-grams in e:

Our method uses agreement information of n-grams , and consensus features are integrated into decoding models.

In Table 5 we show in another dimension the impact of consensus-based features by restricting the maximum order of n-grams used to compute agreement statistics.

One reason could be that the data sparsity for high-order n-grams leads to over fitting on development data.

whose edges correspond to n-grams (weighted with negative log-probabilities) and whose vertices correspond to (n — l)-grams.

This may be regarded as favoring n-grams that are likely to appear in the reference translation (because they are likely in the derivation forest).

However, in order to score well on the BLEU metric for MT evaluation (Papineni et al., 2001), which gives partial credit, we would also like to favor lower-order n-grams that are likely to appear in the reference, even if this means picking some less-likely high-order n-grams .

Now, let us divide N, which contains n-gram types of different n, into several subsets Wn, each of which contains only the n-grams with a given length n. We can now rewrite (19) as follows,

Rank OIflGR using words —-- ——onte‘Carfo usin - rams --» ---d/x 7,‘ Monte Carlo using words w ~ 7 ~ ’ Relative Entropy using N-grams — —~—-’ IRelative EIntropy usin words If r r w

The n-gram based approaches are based on the counts of character or byte n-grams , which are sequences of n characters or bytes, extracted from a corpus for each reference language.

(Dunning, 1994) proposed a system that uses Markov Chains of byte n-grams with Bayesian Decision Rules to minimize the probability error.

(Miller et al., 1999; Song and Croft, 1999) explore the use n-grams in retrieval models.

Subsequently, various types of phrases, such as sequential n-grams (Mitra et al., 1997), head-modifier pairs extracted from syntactic structures (Lewis and Croft, 1990; Zhai, 1997; Dillon and Gray, 1983; Strzalkowski et al., 1994), proximity-based phrases (Turpin and Mof—fat, 1999), were examined with conventional retrieval models (e. g. vector space model).

(Song and Croft, 1999; Miller et al., 1999; Gao et al., 2004; Metzler and Croft, 2005) investigated the effectiveness of language modeling approach in modeling statistical phrases such as n-grams or proximity-based phrases.