Here, we follow the latter work, by combining a coverage score function g with sentence-level compression score functions hl, .

For the compression score function, we follow Martins and Smith (2009) and decompose it as a sum of local score functions pmg defined on dependency arcs:

By designing a quality score function g : {0, 1}N —> R, this can be cast as a global optimization problem with a knapsack constraint:

Then, the following quality score function is defined:

Since our algorithm requires that the objective function is the sum of word score functions , our proposed method has a restriction that we cannot use an arbitrary monotone submodular function as the objective function for the summary.

By formalizing the subtree extraction problem as this new maximization problem, we can treat the constraints regarding the grammaticality of the compressed sentences in a straightforward way and use an arbitrary monotone submodular word score function for words including our word score function (shown later).

The score function is supermodular as a score function of subtree extraction3, because the union of two subtrees can have extra word pairs that are not included in either subtree.

Our score function for a summary 8 is as follows:

We present here an algorithm that runs the parser in pseudo-deterministic mode, greedily choosing at each configuration the transition that maximizes some score function .

Algorithm 1 takes as input a string 21) and a scoring function score() defined over parser transitions and parser configurations.

The scoring function will be the subject of §4 and is not discussed here.

We use a linear model for the score function in Algorithm 1, and define score(t, c) = {I} - gb(t, 0).

Under this framework, we show how to integrate various indicative metrics such as linguistic motivation and query relevance into the compression process by deriving a novel formulation of a compression scoring function .

Our tree-based methods rely on a scoring function that allows for easy and flexible tailoring of sentence compression to the summarization task, ultimately resulting in significant improvements for MDS, while at the same time remaining competitive with existing methods in terms of sentence compression, as discussed next.

postorder) as a sequence of nodes in T, the set L of possible node labels, a scoring function 8 for evaluating each sentence compression hypothesis, and a beam size N. Specifically, O is a permutation on the set {0, l, .

Thus, the decoder is quite flexible — its learned scoring function allows us to incorporate features salient for sentence compression while its language model guarantees the linguistic quality of the compressed string.

The segmentation for an input sentence is decoded by using a joint scoring function combining the two induced models.

Moreover, in order to better combine the strengths of the two models, the proposed approach uses a joint scoring function in a log-linear combination form for the decoding in the segmentation phase.

3.4 The Joint Score Function for Decoding

This paper employs a log-linear interpolation combination (Bishop, 2006) to formulate a joint scoring function based on character-based and word-based models in the decoding:

Each partially lexicalized solution is scored by a battery of scoring functions that compete to generate creative sentences respecting the user specification U, as explained in Section 3.3.

Concerning the scoring of partial solutions and complete sentences, we adopt a simple linear combination of scoring functions .

,fk] be the vector of scoring functions and w = [2120, .