Parse tree: A partial dependency tree 75 E D-trees is a parse tree for a given string wl .

.Qn, we will say it is a projective parse tree for the string.

Final items in this formalism will be those containing some forest F containing a parse tree for some arbitrary string.

Each item contains a piece of information about the sentence’s structure, and a successful parsing process will produce at least one final item containing a full parse tree for the sentence or guaranteeing its existence.

Items in parsing schemata are formally defined as sets of partial parse trees from a set denoted

Trees(G), which is the set of all the possible partial parse trees that do not violate the constraints imposed by a grammar G. More formally, an item set I is defined by Sikkel as a quotient set associated with an equivalence relation on Trees(G).1

A basic approach is template matching on parse trees .

To improve recall, irregularities in parse trees caused by verb form errors are taken into account; to improve precision, n-gram counts are utilized to filter proposed corrections.

To investigate irregularities in parse tree patterns (see §3.2), we utilized the AQUAINT Corpus of English News Text.

We build on the basic approach of template-matching on parse trees in two ways.

To improve recall, irregularities in parse trees caused by verb form errors are considered; to improve precision, n-gram counts are utilized to filter proposed corrections.

Similar strategies with parse trees are pursued in (Bender et al., 2004), and error templates are utilized in (Heidom, 2000) for a word processor.

Relative to verb forms, errors in these categories do not “disturb” the parse tree as much.

The success of this strategy, then, hinges on accurate identification of these items, for example, from parse trees .

In other words, sentences containing verb form errors are more likely to yield an “incorrect” parse tree , sometimes with significant differences.

One goal of this paper is to recognize irregularities in parse trees caused by verb form errors, in order to increase recall.

Among syntax-based translation models, the tree-based approach, which takes as input a parse tree of the source sentence, is a promising direction being faster and simpler than its string-based counterpart.

We have presented a novel forest-based translation approach which uses a packed forest rather than the 1-best parse tree (or k-best parse trees ) to direct the translation.

Using more than one parse tree apparently improves the BLEU score, but at the cost of much slower decoding, since each of the top-k trees has to be decoded individually although they share many common subtrees.

1' (rank of the parse tree picked by the decoder)

Figure 5: Percentage of the i-th best parse tree being picked in decoding.

Informally, a packed parse forest, or forest in short, is a compact representation of all the derivations (i.e., parse trees ) for a given sentence under a context-free grammar (Billot and Lang, 1989).

The parse tree for the preposition case is shown in Figure 2(b) as the l-best parse, while for the conjunction case, the two proper nouns (Basin and Shalong) are combined to form a coordinated NP

Shown in Figure 3(a), these two parse trees can be represented as a single forest by sharing common subtrees such as NPB0,1 and VPB3,6.

Depending on the type of input, these efforts can be divided into two broad categories: the string-based systems whose input is a string to be simultaneously parsed and translated by a synchronous grammar (Wu, 1997; Chiang, 2005; Galley et al., 2006), and the tree-based systems whose input is already a parse tree to be directly converted into a target tree or string (Lin, 2004; Ding and Palmer, 2005; Quirk et al., 2005; Liu et al., 2006; Huang et al., 2006).

However, despite these advantages, current tree-based systems suffer from a major drawback: they only use the 1-best parse tree to direct the translation, which potentially introduces translation mistakes due to parsing errors (Quirk and Corston-Oliver, 2006).

1 A tree sequence refers to an ordered subtree sequence that covers a phrase or a consecutive tree fragment in a parse tree .

Yamada and Knight (2001) use noisy-channel model to transfer a target parse tree into a source sentence.

(2006) propose a feature-based discriminative model for target language syntactic structures prediction, given a source parse tree .

(2006) create an xRS rule headed by a pseudo, non-syntactic nonterminal symbol that subsumes the phrase and its corresponding multi-headed syntactic structure; and one sibling xRS rule that explains how the pseudo symbol can be combined with other genuine non-terminals for acquiring the genuine parse trees .

source and target parse trees T ( fl‘]) and T (ell ) in Fig.

2 illustrates two examples of tree sequences derived from the two parse trees .

and their parse trees T(f1‘]) and T (611 ) 9 the tree

We propose a language model based on a precise, linguistically motivated grammar (a handcrafted Head-driven Phrase Structure Grammar) and a statistical model estimating the probability of a parse tree .

first step in this direction by estimating the probability of a parse tree .

However, our model only looks at the structure of a parse tree and does not take the actual words into account.

As P(T) does not directly apply to parse trees , all possible readings have to be unpacked.

For these lattices the grammar-based language model was simply switched off in the experiment, as no parse trees were produced for efficiency reasons.

(2) Pyram(W) is defined as the probability of the most likely parse tree of a word sequence W: P W = P T 3 gram( ) Tepggefiw) ( > ( ) To determine Pyram(W) is an expensive operation as it involves parsing.

2.2 The Probability of a Parse Tree

The parse trees produced by our parser are binary-branching and rather deep.

(30) For a set S of semantically equivalent2 parse trees for a string ABC, admit the unique parse tree such that at least one of (i) or (ii) holds:

(31) Theorem 1 : For every parse tree oz, there is a semantically equivalent parse-tree N F(a) in which no node resulting from application of B or S functions as the primary functor in a rule application.

(32) Theorem 2: If N F(a) and N F(o/ ) are distinct parse trees , then their model-theoretic interpretations are distinct.

While a detailed description of the respective parsing models is beyond the scope of this paper, it is worth noting that both parsers induce a context free grammar as well as a generative parsing model from a training set of parse trees , and use a development set to tune internal parameters.

One of the main requirements for our dataset is the availability of gold-standard sense and parse tree annotations.

The gold-standard parse tree annotations are required in order to carry out evaluation of parser and PP attachment performance.

Following Atterer and Schutze (2007), we wrote a script that, given a parse tree , identifies instances of PP attachment ambiguity and outputs the (v, n1 , p, n2) quadruple involved and the attachment decision.

Traditionally, parse disambiguation has relied on structural features extracted from syntactic parse trees , and made only limited use of semantic information.

might be incorrect due to errors in English parse trees .

Given a source sentence, the corresponding syntax parse tree T S is first constructed with an English parser.

The other problem comes from the English head word selection error introduced by using source parse trees .

Based on the source syntax parse tree , for each measure word, we identified its head word by using a toolkit from (Chiang and Bikel, 2002) which can heuristically identify head words for sub-trees.

The source head word feature is defined to be a function fl to indicate whether a word ei is the source head word in English according to a parse tree of the source sentence.

In the sentence “He expected to receive a prize for winning,” the path from “win” to its ARGO, “he”, involves the verbs “expect” and “receive” and the preposition “for.” The corresponding path through the parse tree likely occurs a relatively small number of times (or not at all) in the training corpus.

This procedure is quite expensive; we have to copy the entire parse tree at each step, and in general, this procedure could generate an exponential number of transformed parses.

In our case, the AND nodes are similar to constituent nodes in a parse tree — each has a category (e.g.

A transformation rule takes as input a parse tree and produces as output a different, changed parse tree .

In Figure 3 we show for an example from section 22 the parse trees produced by our generative model and our feature-based discriminative model, and the correct parse.

of the parse tree , given the sentence, not joint likelihood of the tree and sentence; and (b) probabilities are normalized globally instead of locally —the graphical models depiction of our trees is undirected.

We define t"(s) to be the set of all possible parse trees for the given sentence licensed by the grammar G.

212,, and a morphological analyzer, we look for the most probable parse tree 7r s.t.

Hence, our parser searches for a parse tree 7r over lexemes (ll H.119) s.t.

Thus our proposed model is a proper model assigning probability mass to all (7r, L) pairs, where 7r is a parse tree and L is the one and only lattice that a sequence of characters (and spaces) W over our alpha-beth gives rise to.

Furthermore, we aim to use the verb class model in NLP tasks, (i) as resource for lexical induction of verb senses, verb alternations, and collocations, and (ii) as a lexical resource for the statistical disambiguation of parse trees .

Figure 1: Example parse tree .

(b) The training tuples are processed: For each tuple, a PCFG parse forest as indicated by Figure l is done, and the Inside-Outside algorithm is applied to estimate the frequencies of the ”parse tree rules”, given the current model probabilities.

Let SE be an English sentence, TE the parse tree of SE, 6 a word of SE, we define the subtree and partial subtree following the definitions in (Ouan-graoua et al., 2007).

If e,-is a descendant of ej in the parse tree , we remove p05,- from PE(e).

Note that the Chinese patterns are not extracted from parse trees .