We propose an alternative approach to generating forests that is based on combining sub-trees within the first best parse through binarization .

Provably, our binarization forest can cover any non-consitituent phrases in a sentence but maintains the desirable property that for each span there is at most one nonterminal so that the grammar constant for decoding is relatively small.

For the purpose of reducing search errors, we apply the synchronous binarization technique to forest-to-string decoding.

To focus on structural variants, we propose a family of binarization algorithms to expand one single constituent tree into a packed forest of binary trees containing combinations of adj acent tree nodes.

0 Forests are not generated by a parser but by combining substructures using a tree binarizer .

For the first time, we show that similar to string-to-tree decoding, synchronous binarization significantly reduces search errors and improves translation quality for forest-to-string decoding.

The motivation of tree binarization is to factorize large and rare structures into smaller but frequent ones to improve generalization.

If long sequences are binarized,

In particular, we integrate synchronous binarizations , verb regrouping, removal of redundant parse nodes, and incorporate a few important features such as translation boundaries.

E T as above-mentioned, such as binarizations , at different levels for constructing partial hypothesis.

We specified a few operators for transforming an elementary tree 7, including flattening tree operators such as removing interior nodes in vi, or grouping the children via binarizations .

Obvious systematic linguistic divergences between language-pairs could be handled by some simple operators such as using binarization to regroup contiguously aligned children.

3.4.1 Binarizations

Binarization of grammars is crucial for improving the complexity and performance of parsing and translation.

We present a versatile binarization algorithm that can be tailored to a number of grammar formalisms by simply varying a formal parameter.

We apply our algorithm to binarizing tree-to-string transducers used in syntax-based machine translation.

Binarization amounts to transforming a given grammar into an equivalent grammar of rank 2, i.e., with at most two nonterminals on any right-hand side.

The ability to binarize grammars is crucial for efficient parsing, because for many grammar formalisms the parsing complexity depends exponentially on the rank of the grammar.

The classical approach to binarization , as known from the Chomsky normal form transformation for context-free grammars (CFGs), proceeds rule by rule.

Note that after binarization , grandparent and sibling information becomes very important in encoding the structure.

This section introduces important implementation details, including supertagging, feature forest pruning and binarization methods.

5.3 Binarization

Since Penn Treebank trees are not binarized, we construct a simple procedure for binarizing them.

Note that the two derivations share the same ( binarized ) tree structure.

Whenever it is possible, binarization of LCFRS rules, or reduction of rank to two, is therefore important for parsing, as it reduces the time complexity needed for dynamic programming.

This has lead to a number of binarization algorithms for LCFRSs, as well as factorization algorithms that factor rules into new rules with smaller rank, without necessarily reducing rank all the way to two.

Kuhlmann and Satta (2009) present an algorithm for binarizing certain LCFRS rules without increasing their fanout, and Sagot and Satta (2010) show how to reduce rank to the lowest value possible for LCFRS rules of fanout two, again without increasing fanout.

We also trained and evaluated on binarized versions of the ordinal GUG labels: a sentence was labeled 1 if the average judgment was at least 3.5 (i.e., would round to 4), and 0 otherwise.

To train our system on binarized data, we replaced the £2 -regularized linear regression model with an 62-regularized logistic regression and used Kendall’s 7' rank correlation between the predicted probabilities of the positive class and the binary gold standard labels as the grid search metric (§3.1) instead of Pearson’s 7“.

We also evaluated the binary system for the ordinal task by computing correlations between its estimated probabilities and the averaged human scores, and we evaluated the ordinal system for the binary task by binarizing its predictions.12

From an initial prediction y, it produces the final prediction: A AM re not affect Pearson’s 'r correlations or rankings, but it would affect binarized predictions.

The system can provide bina-rzied CFG trees in Chomsky Norm Form, and they present a reversible conversion procedure to map arbitrary CFG trees into binarized trees.

In this work, we remain consistent with their work, using the head-finding rules of Zhang and Clark (2008), and the same binarization algorithm.1 We apply the same beam-search algorithm for decoding, and employ the averaged perceptron with early-update to train our model.

Our annotations are binarized recursive word

(Los Angeles)”, have flat structures, and we use “coordination” for their left binarization .

Lastly, for the WSJ40 runs we used a simple, right branching binarization where each active state is annotated with its previous sibling and first child.

Binarization of rules (Earley, 1970) is necessary to obtain cubic parsing time, and closure of unary chains is required for finding total probability mass (rather than just best parses) (Stolcke, 1995).

This was done by collapsing all allowed unary chains to single unary rules, and disallowing multiple unary rule applications over the same span.1 We give the details of our binarization scheme in Section 5.

All productions in the corpus have also been binarized .

Tuning the parameter settings on the development set, we found that parameterized categories, binarization , and including punctuation gave the best F1 performance.

They also binarize the very flat topological tree structures, and prune rules that only occur once.

Most of the literature has been focusing on binarization algorithms, which attempt to find a reduction to 7“ = 2 and return a failure if this is not possible.

(2009) report a general binarization algorithm for LCFRS which, in the case of f = 2, works in time 0(lpl7), where |p| is the size of the input production.

A more efficient binarization algorithm for the case f = 2 is presented in (Gomez-Rodriguez and Satta, 2009), working in time O(|p|).

We present a more precise characterization of the algorithm’s complexity, an optimization analogous to binarization of context-free grammars, and some important implementation details, resulting in an algorithm that is practical for natural-language applications.

We give a more precise complexity analysis in terms of the grammar and the size and maximum degree of the input graph, and we show how to optimize it by a process analogous to binarization of CFGs, following Gildea (2011).

In this section, we present a refinement that makes the rule-matching procedure explicit, and because it matches rules little by little, similarly to binarization of CFG rules, it does so more efliciently than the original.